Michael Huemer

Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes.

Abstract: In earlier work, I argued that individuals have a right to own firearms for personal defense, and that as a result, gun prohibition would be unjustified unless it at least produced benefits many times greater than its costs. Here, I defend that argument against objections posed by Nicholas Dixon and Jeff McMahan to the effect that the right of citizens to be free from gun violence counterbalances the right of self-defense, and that gun prohibition does not violate the right of self-defense because it renders everyone overall safer. (4258 words)

Paradox Lost covers ten of philosophy’s most fascinating paradoxes, in which seemingly compelling reasoning leads to absurd conclusions. The following paradoxes are included: The Liar Paradox, in which a sentence says of itself that it is false. Is the sentence true or false? The Sorites Paradox, in which we imagine removing grains of sand one at a time from a heap of sand. Is there a particular grain whose removal converts the heap to a non-heap? The Puzzle of the Self-Torturer, in which a series of seemingly rational choices has us accepting a life of excruciating pain, in exchange for millions of dollars. Newcomb’s Problem, in which we seemingly maximize our expected profit by taking an unknown sum of money, rather than taking the same sum plus $1000. The Surprise Quiz Paradox, in which a professor finds that it is impossible to give a surprise quiz on any particular day of the week... but also that if this is so, then a surprise quiz can be given on any day. The Two Envelope Paradox, in which we are asked to choose between two indistinguishable envelopes, and it is seemingly shown that each envelope is preferable to the other. The Ravens Paradox, in which observing a purple shoe provides evidence that all ravens are black. The Shooting Room Paradox, in which a deadly game kills 90% of all who play, yet each individual’s survival turns on the flip of a fair coin. Each paradox is clearly described, common mistakes are explored, and a clear, logical solution offered. Paradox Lost will appeal to professional philosophers, students of philosophy, and all who love intellectual puzzles.

Beauty is put to sleep and woken up either once or twice, depending on the flip of a coin; after each waking, she will fall asleep and forget having woken. Upon waking, what should be her credence that the coin came up heads? Some say 1/2; others say 1/3. I propose that evidence supports a theory for you when your having that qualitative evidence would be more likely if the theory were true than if it were false. This view supports the “1/3” answer to the Sleeping Beauty problem. It also has applications to other arguments concerning self-locating beliefs: the Doomsday Argument fails, and the Fine Tuning Argument supports the Multiverse theory, if and only if it would be metaphysically possible for you to exist in a different universe.

Den Beteiligten des Politikbetriebs einschließlich Wählern, Aktivisten und Spitzenpolitikern fehlt häufig der grundlegende Sachverstand für die jeweiligen politischen Entscheidungen. Selbst Experten verstehen gesellschaftliche Mechanismen kaum und können deren Auswirkung kaum vorhersagen. Nur auf einfachste und unstrittige politische Behauptungen ist Verlass. Teilweise rührt das daher, dass politisches Wissen schwer zu erlangen ist, und teilweise daher, dass der Einzelne keinen ausreichenden Ansporn hat, es zu erlangen. Demzufolge besteht der beste Ratschlag an die politischen Akteure sehr häufig schlicht darin, gesellschaftliche Probleme nicht anzugehen, zumal Eingriffe, die nicht auf einem genauen Verständnis beruhen, vermutlich mehr Schaden als Nutzen anrichten. [This is a German translation of "In Praise of Passivity". Studia Humana 1,2 (2012): 12-28.]

Soll der Freizeitkonsum von Drogen wie Marihuana, Kokain, Heroin und LSD einem gesetzlichen Verbot unterliegen? Drogengegner sagen ja. Sie behaupten für gewöhnlich, Drogenkonsum sei sowohl für den Nutzer als auch für die Gesellschaft allgemein äußerst schädlich – vielleicht sogar unmoralisch, und sie glauben, diese Tatsachen seien als Verbotsgrund ausreichend. Freigabebefürworter sagen nein und berufen sich dabei für gewöhnlich auf eines oder mehrere von drei Argumenten: Erstens behaupten einige, Drogenkonsum sei nicht so schädlich, wie Drogengegner meinen, und sei gelegentlich sogar nützlich. Zweitens behaupten einige, Drogenverbote „funktionierten“ nicht, d. h. sie verhinderten den Drogenkonsum nicht besonders wirksam und hätten eine Reihe sehr nachteiliger Folgewirkungen. Schließlich behaupten einige, Drogenverbote seien Unrecht oder verletzten Rechte. Ich unternehme an dieser Stelle nicht den Versuch, all diese Argumente zu besprechen. Stattdessen beschränke ich mich auf die drei Hauptargumente der Drogendebatte: Erstens demjenigen, Drogen solle man aufgrund der Schädigung der Konsumenten verbieten; zweitens, man solle sie verbieten, weil sie außer den Konsumenten noch anderen schadeten; und drittens, man solle sie legalisieren, weil Drogenverbote Rechte verletzten. Ich richte mein Augenmerk auf die moralphilosophischen Fragen, welche diese Argumente aufwerfen, statt auf medizinische oder gesellschaftliche Fragen und werde zeigen, dass die beiden Verbotsargumente scheitern, wogegen das dritte Argument für die Freigabe greift. [This is a German translation of "America's Unjust Drug War". In The New Prohibition, ed. Bill Masters (St. Louis, Mo.: Accurate Press, 2004), p. 133-144.]

Menschen haben ein Anscheinsrecht (engl. prima facie right), Schusswaffen zu besitzen. Dieses Recht ist bedeutsam sowohl in Hinblick auf die Rolle, die Waffenbesitz im Leben von Waffenbegeisterten spielt, als auch auf den Selbstverteidigungsnutzen von Schusswaffen. Dieses Recht wird auch nicht durch den gesellschaftlichen Schaden privaten Waffenbesitzes verdrängt. Dieser Schaden wurde stark aufgebauscht und ist vermutlich erheblich kleiner als der Nutzen privaten Waffenbesitzes. Und ich lege dar, dass der Schaden den Nutzen um ein Vielfaches übertreffen müsste, um ein Verbot von Schusswaffen zu rechtfertigen. [This is a German translation of: „Is There a Right to Own a Gun?“, Social Theory and Practice, Vol. 29, No. 2 (April 2003), pp. 297-324.]

Einwanderungsbeschränkungen verletzen das Anscheinsrecht (engl. prima facie right) Einwanderungswilliger, keinem schädlichem Zwang ausgesetzt zu werden. Dieses Anscheinsrecht wird nicht durch die wirtschaftlichen, fiskalischen und kulturellen Folgen der Einwanderung entkräftet oder verdrängt – und auch nicht durch die besondere Pflicht, welche der Staat gegenüber seinen eigenen Bürgern und speziell den Ärmsten unter ihnen hat. Er hat gleichfalls kein Recht, Bedingungen für die Staatsbürgerschaft in gleicher Weise aufzustellen, wie dies private Clubs als Voraussetzung für die Mitgliedschaft tun. [This is a German translation of: „Is There a Right to Immigrate?“, Social Theory and Practice, Vol. 36, No. 3 (2010), pp. 429-61.]

A four-part series of dialogues between two philosophy students, M and V. The question: is it wrong to eat meat? M and V review the standard arguments plus a few new ones. Part 2 discusses miscellaneous defenses of meat-eating. These include the claim that the consumer is not responsible for wrongs committed by farm workers, that a single individual cannot have any effect on the meat industry, that farm animals are better off living on factory farms than never existing at all, that we can’t be sure animals feel pain, that animals can justly be eaten since they eat each other, that meat-eating is natural, that morality only protects those who can understand morality, that morality only protects members of society, and that only humans possess souls.

The justificatory force of empirical reasoning always depends upon the existence of some synthetic, a priori justification. The reasoner must begin with justified, substantive constraints on both the prior probability of the conclusion and certain conditional probabilities; otherwise, all possible degrees of belief in the conclusion are left open given the premises. Such constraints cannot in general be empirically justified, on pain of infinite regress. Nor does subjective Bayesianism offer a way out for the empiricist. Despite often-cited convergence theorems, subjective Bayesians cannot hold that any empirical hypothesis is ever objectively justified in the relevant sense. Rationalism is thus the only alternative to an implausible skepticism.

Individuals have a prima facie right to own firearms. This right is significant in view both of the role that such ownership plays in the lives of firearms enthusiasts and of the self-defense value of firearms. Nor is this right overridden by the social harms of private gun ownership. These harms have been greatly exaggerated and are probably considerably smaller than the benefits of private gun ownership. And I argue that the harms would have to be at least several times greater than the benefits in order to render gun prohibition permissible.

Recent results in probability theory have cast doubt on coherentism, purportedly showing (a) that coherence among a set of beliefs cannot raise their probability unless individual beliefs have some independent credibility, and (b) that no possible measure of coherence makes coherence generally probability-enhancing. I argue that coherentists can reject assumptions on which these theorems depend, and I derive a general condition under which the concurrence of two information sources lacking individual credibility can raise the probability of what they report.

Sense data are the alleged mind-dependent objects that we are directly aware of in perception, and that have exactly the properties they appear to have. For instance, sense data theorists say that, upon viewing a tomato in normal conditions, one forms an image of the tomato in one's mind. This image is red and round. The mental image is an example of a “sense datum.” Many philosophers have rejected the notion of sense data, either because they believe that perception gives us direct awareness of physical phenomena, rather than mere mental images, or because they believe that the mental phenomena involved in perception do not have the properties that appear to us (for instance, I might have a visual experience representing a red, round tomato, but my experience is not itself red or round). Defenders of sense data have argued, among other things, that sense data are required to explain such phenomena as perspectival variation, illusion, and hallucination. Critics of sense data have objected to the theory's commitment to mind-body dualism, the problems it raises for our knowledge of the external world, its difficulty in locating sense data in physical space, and its apparent commitment to the existence of objects with indeterminate properties

Trenton Merricks argues that on any reasonable account, warrant must entailtruth. I demonstrate three theses about the properties ofwarrant: (1) Warrant is not unique;there are many properties that satisfy the definition of warrant. (2) Warrant need not entail truth; there are some warrant properties that entailtruthand others that do not. (3) Warrant need not be closed under entailment, even if knowledge is. If knowledge satisfies closure, then some warrant properties satisfy closure while others do not;if knowledge violates closure, then allwarrant properties violate closure.

People want things, and they tend to act in such a way as to get the things they want, to the best of their ability.1 Sometimes our wants conflict with each other, so that we are forced to choose between different things that we want. When this happens, we normally choose the thing that we want more, over the thing that we want less. Behaving in this way is what we call “rational”; more specifically, it is “instrumentally rational.” Instrumental rationality consists in choosing the means that best achieves one’s goals, according to the information one has.