The bounded proper forcing axiom BPFA is the statement that for any family of ℵ 1 many maximal antichains of a proper forcing notion, each of size ℵ 1 , there is a directed set meeting all these antichains. A regular cardinal κ is called Σ 1 -reflecting, if for any regular cardinal χ, for all formulas $\varphi, "H(\chi) \models`\varphi'"$ implies " $\exists\delta . We investigate several algebraic consequences of BPFA, and we show that the consistency strength of the bounded (...) proper forcing axiom is exactly the existence of a Σ 1 -reflecting cardinal (which is less than the existence of a Mahlo cardinal). We also show that the question of the existence of isomorphisms between two structures can be reduced to the question of rigidity of a structure. (shrink)

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Model Theory in Logic and Philosophy of Logic

Philosophy of Mathematics

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We reimplement the creature forcing construction used by Fischer et al. :1045–1103, 2017. https://doi.org/10.1007/S00153-017-0553-8. arXiv:1402.0367 [math.LO]) to separate Cichoń’s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction by adding uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.

If ZFC is consistent, then each of the following is consistent with ZFC + 2ℵ0 = ℵ2: (1) $X \subseteq \mathbb{R}$ is of strong measure zero iff |X| ≤ ℵ1 + there is a generalized Sierpinski set. (2) The union of ℵ1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size ℵ2 + there is no Cohen real over L.

We use a creature construction to show that consistently $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$The same method shows the consistency of $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$.

We give a self-contained proof of the preservation theorem for proper countable support iterations known as “tools-preservation”, “Case A” or “first preservation theorem” in the literature. We do not assume that the forcings add reals.

1. If A is strongly amorphous , then its power set P is dually Dedekind infinite, i. e., every function from P onto P is injective. 2. The class of “inexhaustible” sets is not closed under supersets unless AC holds.

We investigate the Ramsey theory of continuous graph-structures on complete, separable metric spaces and apply the results to the problem of covering a plane by functions. Let the homogeneity number[Formula: see text] of a pair-coloring c:[X]2→2 be the number of c-homogeneous subsets of X needed to cover X. We isolate two continuous pair-colorings on the Cantor space 2ω, c min and c max, which satisfy [Formula: see text] and prove: Theorem. For every Polish space X and every continuous pair-coloringc:[X]2→2with[Formula: see (...) text], [Formula: see text] There is a model of set theory in which[Formula: see text]and[Formula: see text]. The consistency of [Formula: see text] and of [Formula: see text] follows from [20]. We prove that [Formula: see text] is equal to the covering number of 2 by graphs of Lipschitz functions and their reflections on the diagonal. An iteration of an optimal forcing notion associated to c min gives: Theorem. There is a model of set theory in which ℝ2 is coverable byℵ1graphs and reflections of graphs of continuous real functions; ℝ2 is not coverable byℵ1graphs and reflections of graphs of Lipschitz real functions. Figure 1.1 in the introduction summarizes the ZFC results in Part I of the paper. The independence results in Part II show that any two rows in Fig. 1.1 can be separated if one excludes [Formula: see text] from row. (shrink)

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new [Formula: see text]-sequences (for some regular [Formula: see text]). As an application, we show that consistently the following cardinal characteristics can be different: The (“independent”) characteristics in Cichoń’s diagram, plus [Formula: see text]. (So we get thirteen different values, including [Formula: see text] and continuum). We also give constructions to alternatively separate other MA-numbers (instead of [Formula: see text]), namely: MA for [Formula: see (...) text]-Knaster from MA for [Formula: see text]-Knaster; and MA for the union of all [Formula: see text]-Knaster forcings from MA for precaliber. (shrink)

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new <κ-sequences. As an application, we show that consistently the followi...

Reviewed Works:Tomek Bartoszynski, Marion Scheepers, Set Theory, Annual Boise Extravaganza in Set Theory Conference, March 13-15, 1992, April 10-11, 1993, March 25-27, 1994, Boise State University, Boise, Idaho.R. Aharoni, A. Hajnal, E. C. Milner, Interval Covers of a Linearly Ordered Set.Eyal Amir, Haim Judah, Souslin Absoluteness, Uniformization and Regularity Properties of Projective Sets.Tomek Bartoszynski, Ireneusz Reclaw, Not Every $\gamma$-Set is Strongly Meager.Andreas Blass, Reductions Between Cardinal Characteristics of the Continuum.Claude Laflamme, Filter Games and Combinatorial Properties of Strategies.R. Daniel Mauldin, Analytic (...) non-Borel Sets Modulo Null Sets.Janusz Pawlikowski, Laver's Forcing and Outer Measure.Marion Scheepers, Meager Sets and Infinite Games.Saharon Shelah, On Some Problems in General Topology.Saharon Shelah, Remarks on $\aleph_1$-CWH not CWH First Countable Spaces.Juris Steprans, Cardinal Invariants Associated with Hausdorff Capacities. (shrink)

We show that it is consistent that the reaping number r is less than u , the size of the smallest base for an ultrafilter. To show that our forcing preserves certain ultrafilters, we prove a general partition theorem involving Ramsey ideals.

A long-standing theme in discussion of perception and thought has been that our primary cognitive contact with individual objects and events in the world derives from our perceptual contact with them. When I look at a duck in front of me, I am not merely presented with the fact that there is at least one duck in the area, rather I seem to be presented withthisthing (as one might put it from my perspective) in front of me, which looks to (...) me to be a duck. Furthermore, such a perception would seem to put me in a position not merely to make the existential judgment that there is some duck or other present, but rather to make a singular, demonstrative judgment, that that is a duck. My grounds for an existential judgment in this case derives from my apprehension of the demonstrative thought and not vice versa. (shrink)

On Inception is a translation of Martin Heidegger's Gesamtausgabe 70. This work belongs to the crucial period, before and during WWII, when Heidegger was at work on a series of treatises that begins with "Contributions to Philosophy" and includes "The Event" and "The History of Beyng." These works are difficult, even hermetic, but represent a crucial development in Heidegger's thinking. On Inception deepens the investigation underway in the other volumes of the series and provides a unique perspective on Heidegger's (...) thinking of Being and of Event. Here, Heidegger asks, with a greater insistence than anywhere else in his work, what it might mean to think of being as event, and not as presence. Event cannot be thought without the sense of a beginning - an inception - and so, Heidegger insists, we must try to think of being as inception, as fundamentally inceptive. On Inception pursues rigorously the difficult and puzzling implications of this speculation. It does not merely extend work already undertaken but also opens doors onto wholly other pathways. (shrink)

Is it OK to lie to Siri? Is it bad to mistreat a robot for our own pleasure? Under what condition should we grant a moral status to an artificial intelligence (AI) system? This paper looks at different arguments for granting moral status to an AI system: the idea of indirect duties, the relational argument, the argument from intelligence, the arguments from life and information, and the argument from sentience. In each but the last case, we find unresolved issues with (...) the particular argument, which leads us to move to a different one. We leave the idea of indirect duties aside since these duties do not imply considering an AI system for its own sake. The paper rejects the relational argument and the argument from intelligence. The argument from life may lead us to grant a moral status to an AI system, but only in a weak sense. Sentience, by contrast, is a strong argument for the moral status of an AI system—based, among other things, on the Aristotelian principle of equality: that same cases should be treated in the same way. The paper points out, however, that no AI system is sentient given the current level of technological development. (shrink)

Over the past three decades, the philosophy of biology has emerged from the shadow of the philosophy of physics to become a respectable and thriving philosophical subdiscipline. The authors take a fresh look at the life sciences and the philosophy of biology from a strictly realist and emergentist-naturalist perspective. They outline a unified and science-oriented philosophical framework that enables the clarification of many foundational and philosophical issues in biology. This book will be of interest both to life scientists and philosophers.

We provide a battery of examples of delusions against which theoretical accounts can be tested. Then, we identify neuropsychological anomalies that could produce the unusual experiences that may lead, in turn, to the delusions in our battery. However, we argue against Maher’s view that delusions are false beliefs that arise as normal responses to anomalous experiences. We propose, instead, that a second factor is required to account for the transition from unusual experience to delusional belief. The second factor in the (...) aetiology of delusions can be described superficially as a loss of the ability to reject a candidate for belief on the grounds of its implausibility and its inconsistency with everything else that the patient knows. But we point out some problems that confront any attempt to say more about the nature of this second factor. (shrink)

Martin Heidegger's Contributions to Philosophy reflects his famous philosophical "turning." In this work, Heidegger returns to the question of being from its inception in Being and Time to a new questioning of being as event.

What exactly is hope and how does it influence our decisions? In How We Hope, Adrienne Martin presents a novel account of hope, the motivational resources it presupposes, and its function in our practical lives. She contends that hoping for an outcome means treating certain feelings, plans, and imaginings as justified, and that hope thereby involves sophisticated reflective and conceptual capacities. Martin develops this original perspective on hope--what she calls the "incorporation analysis"--in contrast to the two dominant philosophical (...) conceptions of hope: the orthodox definition, where hoping for an outcome is simply desiring it while thinking it possible, and agent-centered views, where hoping for an outcome is setting oneself to pursue it. In exploring how hope influences our decisions, she establishes that it is not always a positive motivational force and can render us complacent. She also examines the relationship between hope and faith, both religious and secular, and identifies a previously unnoted form of hope: normative or interpersonal hope. When we place normative hope in people, we relate to them as responsible agents and aspire for them to overcome challenges arising from situation or character. Demonstrating that hope merits rigorous philosophical investigation, both in its own right and in virtue of what it reveals about the nature of human emotion and motivation, How We Hope offers an original, sustained look at a largely neglected topic in philosophy. (shrink)

Martin Heidegger is one of the most important and influential philosophers of the 20th Century. A major figure in the development of phenomenology, his work also profoundly influenced many of the intellectual movements that followed in his wake, from Sartre's Existentialism to Derrida's deconstructionism. Towards the Definition of Philosophy brings together two seminal lectures that mark a breakthrough moment in Heidegger's thought and introduces the major themes that he would develop in his opus Being and Time.

Eric Martin and Daniel N. Osherson present a theory of inductive logic built on model theory. Their aim is to extend the mathematics of Formal Learning Theory to a more general setting and to provide a more accurate image of empirical inquiry. The formal results of their study illuminate aspects of scientific inquiry that are not covered by the commonly applied Bayesian approach.

A landmark discussion between two great thinkers, vital to an understanding of twentieth-century philosophy and intellectual history.

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an argument against the (...) second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)

This paper proposes a view of time that takes passage to be the most basic temporal notion, instead of the usual A-theoretic and B-theoretic notions, and explores how we should think of a world that exhibits such a genuine temporal passage. It will be argued that an objective passage of time can only be made sense of from an atemporal point of view and only when it is able to constitute a genuine change of objects across time. This requires that (...) passage can flip one fact into a contrary fact, even though neither side of the temporal passage is privileged over the other. We can make sense of this if the world is inherently perspectival. Such an inherently perspectival world is characterized by fragmentalism, a view that has been introduced by Fine in his ‘Tense and Reality’ (2005). Unlike Fine's tense-theoretic fragmentalism though, the proposed view will be a fragmentalist view based in a primitive notion of passage. (shrink)

An essential all-in-one introduction, Ethics for Engineers provides in-depth coverage of major ethical theories, professional codes of ethics, and case studies in a single volume. Incorporating numerous practical examples and about 100 review questions, it helps students better understand and address ethical issues that they may face in their future careers. Topics covered include whistle-blowing, the problem of many hands, gifts, bribes, conflicts of interest, engineering and environmental ethics, privacy and computer ethics, ethical technology assessment, and the ethics of cost-benefit (...) analysis and risk and uncertainty. (shrink)

The Liar paradox arises when we consider a sentence that says of itself that it is not true. If such self-referential sentences exist? and examples like?This sentence is not true? certainly suggest this?, then our logic and standard notion of truth allow to infer a contradiction: The Liar sentence is true and not true. What has gone wrong? Must we revise our notion of truth and our logic? Or can we dispel the common conviction that there are such self-referential sentences? (...) The present study explores the second path.0After comparing the Liar reasoning in formal and informal logic and showing that there are no Gödelian Liar sentences, the study moves on from the semantics of self-reference to the metaphysics of expressions and proposes a novel solution to the Liar paradox: Meaningful expressions are distinct from their syntactic bases and exist only relative to contexts. Detailed semantico-metaphysical arguments show that in this dynamic setting, an object can be referred to only after it has started to exist. Hence the circular reference needed in the Liar paradox cannot occur, after all. As this solution is contextualist, it evades the expressibility problems of other proposals. (shrink)

This book provides the first systematic presentation of anthropology's 'ontological turn', placing it in the landscape of contemporary social theory.

_ Source: _Volume 6, Issue 2-3, pp 120 - 142 This paper aims to contribute to the debate over epistemic versus non-epistemic readings of the ‘hinges’ in Wittgenstein’s _On Certainty_. I follow Marie McGinn’s and Daniele Moyal-Sharrock’s lead in developing an analogy between mathematical sentences and certainties, and using the former as a model for the latter. However, I disagree with McGinn’s and Moyal-Sharrock’s interpretations concerning Wittgenstein’s views of both relata. I argue that mathematical sentences as well as certainties are (...) true and are propositions; that some of them can be epistemically justified; that in some senses they are not prior to empirical knowledge; that they are not ineffable; and that their primary function is epistemic as much as it is semantic. (shrink)

Humanity has reached a critical moment. Our world is unsettled and rapidly changing, and we face existential risks over the next century. Various outcomes--good and bad--are possible. Yet our approach to the future is characterized by short-term thinking, polarizing debates, alarmist rhetoric, and pessimism. In this short, exhilarating book, renowned scientist and bestselling author Martin Rees argues that humanity's prospects depend on our taking a very different approach to planning for tomorrow. The future of humanity is bound to the (...) future of science and hinges on how successfully we harness technological advances to address our challenges. If we are to use science to solve our problems while avoiding its dystopian risks, we must think rationally, globally, collectively, and optimistically about the long term. Advances in biotechnology, cybertechnology, robotics, and artificial intelligence--if pursued and applied wisely--could empower us to boost the developing and developed world and overcome the threats humanity faces on Earth, from climate change to nuclear war. At the same time, further advances in space science will allow humans to explore the solar system and beyond with robots and AI. But there is no "Plan B" for Earth--no viable alternative within reach if we do not care for our home planet. Rich with fascinating insights into cutting-edge science and technology, this accessible book will captivate anyone who wants to understand the critical issues that will define the future of humanity on Earth and beyond."-- Provided by publisher. (shrink)

Richard Rorty (1931 - 2007) ist einer der wichtigsten amerikanischen Philosophen der Gegenwart, der die analytische Philosophie sowohl geprägt als auch maßgeblich zu ihrer Kritik beigetragen und damit die Wiederentdeckung des Pragmatismus vorangetrieben hat. In diesem Handbuch werden alle wichtigen Aspekte seines Lebens und seiner philosophischen Arbeit dargestellt und einer wissenschaftlichen Diskussion unterzogen.

Material from this paper appears in Chap. 7 of my book Reason and Being, but there is also stuff here that isn't in the book. In particular, it discusses the claims that, for Spinoza, conceiving implies explaining and that existence is identical to or reducible to conceivability. So, if you're interested in those issues, this paper might be worth a read.

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data will (...) run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data. (shrink)

Objects often manifest themselves in incompatible ways across perspectives that are epistemically on a par. The standard response to such cases is to deny that the properties that things appear to have from different perspectives are properties that things really have out there. This type of response seems worrying: too many properties admit of perspectival variance and there are good theoretical reasons to think that such properties are genuinely instantiated. So, we have reason to explore views on which things can (...) have the incompatible properties they appear to have across perspectives. This paper explores the view that things can have incompatible properties if the world is not a metaphysically unified place but is instead fragmented. There is a sensible notion of co-obtainment, on which two facts can each obtain without co-obtaining. Using this notion, we can step back from our embedded perspectives on the world without deeming the contents of those perspectives to be mere appearances. This renders th.. (shrink)

Cognitive approaches contribute to our understanding of delusions by providing an explanatory framework that extends beyond the personal level to the sub personal level of information-processing systems. According to one influential cognitive approach, two factors are required to account for the content of a delusion, its initial adoption as a belief, and its persistence. This chapter reviews Bayesian developments of the two-factor framework.

Anosognosia is literally ‘unawareness of or failure to acknowledge one’s hemi- plegia or other disability’ (OED). Etymology would suggest the meaning ‘lack of knowledge of disease’ so that anosognosia would include any denial of impairment, such as denial of blindness (Anton’s syndrome). But Babinski, who introduced the term in 1914, applied it only to patients with hemiplegia who fail to acknowledge their paralysis. Most commonly, this is failure to acknowledge paralysis of the left side of the body following damage to (...) the right hemisphere of the brain. In this paper, we shall mainly be concerned with anosognosia for hemiplegia. But we shall also use the term ‘anosognosia’ in an inclusive way to encompass lack of knowledge or acknowledgement of any impairment. Indeed, in the construction ‘anosognosia for X’, X might even be anosognosia for some Y. (shrink)