Skip to main content Accessibility help
×
  1. Home
  2. Browse subjects
  3. Philosophy
  4. Logic
  5. Content listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

4138 results in Logic

Page 146 of 207

  • Foreword

  • Ian Hacking, University of Toronto
  • Book:
    An Introduction to Probability and Inductive Logic
    Published online:
    05 June 2012
    Print publication:
    02 July 2001, pp xi-xiv

  • Summary

    Inductive logic is unlike deductive or symbolic logic. In deductive reasoning, when you have true premises and a valid argument, the conclusion must be true too. Valid deductive arguments do not take risks.

    Inductive logic takes risks. You can have true premises, a good argument, but a false conclusion. Inductive logic uses probability to analyse that kind of risky argument.

    Good News

    Inductive reasoning is a guide in life. People make risky decisions all the time. It plays a much larger part in everyday affairs than deductive reasoning.

    Bad News

    People are very bad when reasoning about risks. We make a lot of mistakes when we use probabilities.

    This book starts with a list of seven Odd Questions. They look pretty simple. But most people get some of the answers wrong. The last group of nine-year-olds I tested did better than a group of professors. Try the Odd Questions. Each one is discussed later in the book.

    Practical Aims

    This book can help you understand, use, and act on probabilities, risks, and statistics. We live our lives taking chances, acting when we don't know enough. Every day we experience a lot of uncertainties. This book is about the kinds of actions you can take when you are uncertain what to do. It is about the inferences you can draw when your evidence leaves you unsure what is true.

  • 4 - Elementary Probability Ideas

  • from HOW TO CALCULATE PROBABILITIES
  • Ian Hacking, University of Toronto
  • Book:
    An Introduction to Probability and Inductive Logic
    Published online:
    05 June 2012
    Print publication:
    02 July 2001, pp 37-46

  • Summary

    This chapter explains the usual notation for talking about probability, and then reminds you how to add and multiply with probabilities.

    WHAT HAS A PROBABILITY?

    Suppose you want to take out car insurance. The insurance company will want to know your age, sex, driving experience, make of car, and so forth. They do so because they have a question in mind:

    What is the probability that you will have an automobile accident next year?

    That asks about a proposition (statement, assertion, conjecture, etc.):

    “You will have an automobile accident next year.”

    The company wants to know: What is the probability that this proposition is true?

    The insurers could ask the same question in a different way:

    What is the probability of your having an automobile accident next year?

    This asks about an event (something of a certain sort happening). Will there be “an automobile accident next year, in which you are driving one of the cars involved”?

    The company wants to know: What is the probability of this event occurring?

    Obviously these are two different ways of asking the same question.

    PROPOSITIONS AND EVENTS

    Logicians are interested in arguments from premises to conclusions. Premises and conclusions are propositions. So inductive logic textbooks usually talk about the probability of propositions.

    Most statisticians and most textbooks of probability talk about the probability of events.

    So there are two languages of probability, propositions and events.

  • 3 - The Gambler's Fallacy

  • from HOW TO CALCULATE PROBABILITIES
  • Ian Hacking, University of Toronto
  • Book:
    An Introduction to Probability and Inductive Logic
    Published online:
    05 June 2012
    Print publication:
    02 July 2001, pp 23-36

  • Summary

    Most of the main ideas about probability come up right at the beginning. Two major ones are independence and randomness. Even more important for clear thinking is the notion of a probability model.

    ROULETTE

    A gambler is betting on what he thinks is a fair roulette wheel. The wheel is divided into 38 segments, of which:

  • ▪ 18 segments are black.

  • ▪ 18 segments are red.

  • ▪ 2 segments are green, and marked with zeroes.

    • If you bet $10 on red, and the wheel stops at red, you win $20. Likewise if you bet $10 on black and it stops at black, you win $20. Otherwise you lose. The house always wins when the wheel stops at zero.

    Now imagine that there has been a long run–a dozen spins–in which the wheel stopped at black. The gambler decides to bet on red, because he thinks:

    The wheel must come up red soon.

    This wheel is fair, so it stops on red as often as it stops on black.

    Since it has not stopped on red recently, it must stop there soon. I'll bet on red.

    The argument is a risky one. The conclusion is, “The wheel must stop on red in the next few spins.” The argument leads to a risky decision. The gambler decides to bet on red. There you have it, an argument and a decision. Do you agree with the gambler?

  • 13 - Personal Probabilities

  • from PROBABILITY AS A MEASURE OF BELIEF
  • Ian Hacking, University of Toronto
  • Book:
    An Introduction to Probability and Inductive Logic
    Published online:
    05 June 2012
    Print publication:
    02 July 2001, pp 151-162

  • Summary

    How personal degrees of belief can be represented numerically by using imaginary gambles.

    Chapters 1–10 were often deliberately ambiguous about different kinds of probability. That was because the basic ideas usually applied, across the board, to most kinds of probability.

    Now we develop ideas that matter a lot for belief-type probabilities. They do not matter so much from the frequency point of view.

    THE PROGRAM

    There are three distinct steps in the argument, and each deserves a separate chapter.

  • ▪ This chapter shows how you might use numbers to represent your degrees of belief.

  • ▪ Chapter 14 shows why these numbers should satisfy the basic rules of probability. (And hence they should obey Bayes' Rule.)

  • ▪ Chapter 15 shows how to use Bayes' Rule to revise or update personal probabilities in the light of new evidence. This is the fundamental motivation for the group of chapters, 13–15.

    • In these chapters we are concerned with a person's degrees of belief. We are talking about personal probabilities. But this approach can be used for other versions of belief-type probability, such as the logical perspective of Keynes and Carnap.

    Because Bayes' Rule is so fundamental, this approach is often called Bayesian. “Belief dogmatists” are often simply called Bayesians because the use of Bayes' rule as a model of learning from experience plays such a large part in their philosophy. But notice that there are many varieties of Bayesian thinking. This perspective ranges from the personal to the logical.

  • 9 - Maximizing Expected Value

  • from HOW TO COMBINE PROBABILITIES AND UTILITIES
  • Ian Hacking, University of Toronto
  • Book:
    An Introduction to Probability and Inductive Logic
    Published online:
    05 June 2012
    Print publication:
    02 July 2001, pp 98-113

  • Summary

    How do you choose among possible acts? The most common decision rule is an obvious one. Perform the action with the highest expected value. There are, however, a few more paradoxes connected with this simple rule.

    RISKY DECISIONS

    Logic analyzes reasons and arguments. We can give reasons for our beliefs. We can also give reasons for our actions and our decisions. What is the best thing to do under the circumstances? Inductive logic analyzes risky arguments. It also helps with decision theory, the theory of making risky decisions.

    Should I go out in a thunderstorm to fetch a book, even though I am scared of lightning? I go out in a thunderstorm because I believe I left a book outside. I believe it will get wet and be ruined. I also believe I will not be struck by lightning. But I also go outside because I want the book, among other things. Of course, my beliefs are not certainties–I am pretty confident I left the book there. I am pretty sure it will get wet if it is there. I know it is not probable that I will be hit by lightning.

    Decisions depend on two kinds of thing:

  • ▪ What we believe.

  • ▪ What we want.

    • Sometimes we can represent our degrees of belief or confidence by probabilities. Sometimes we can represent what we want by dollar values, or at least by judgments of value, which we call utilities.

  • 4 - A Consequentialist Theory of Virtue

  • Julia Driver, Dartmouth College, New Hampshire
  • Book:
    Uneasy Virtue
    Published online:
    22 July 2009
    Print publication:
    23 April 2001, pp 63-83

  • Summary

    Consequentialist theories of virtue have been proposed before. David Hume's theory, for example, while not completely consequentialist in nature, draws a compelling connection between utility and virtue. Virtue produces pleasure, and one mechanism of that production is our appreciation of the virtues as socially useful. Benevolence, for example, gains its merit in part from “its tendency to promote the interests of our species and bestow happiness on human society” (Hume 1983, p. 20) The analysis is extended to justice – though in the case of justice “… reflections on the beneficial consequences of this virtue are the sole foundation of its merit …” (ibid.). The value or merit of benevolence, on the other hand, is only partly due to its usefulness:

    As a certain proof, that the whole merit of benevolence is not derived from its usefulness, we may observe, that, in a kind way of blame, we say, a person is too good; when he exceeds his part in society, and carries his attention for others beyond the proper bounds.

    (Ibid, p. 66)

    Thus, when the benevolence becomes excessive it is no longer useful, yet it is still regarded as a virtue by Hume. The merit of benevolence must be derived in part from some naturally pleasing quality it has.

    But Hume, in this passage, did not consider another explanation for the “kind way of blame.” The trait ‘benevolence’ can, generally speaking, produce good or useful consequences, and thus be a virtue, while occasionally breaking down.

  • 2 - The Virtues of Ignorance

  • Julia Driver, Dartmouth College, New Hampshire
  • Book:
    Uneasy Virtue
    Published online:
    22 July 2009
    Print publication:
    23 April 2001, pp 16-41

  • Summary

    There is a class of moral virtues that either doesn't require that the agent know that what she is doing is right or, worse, that actually requires that the agent be ignorant. These virtues I am calling the ‘virtues of ignorance.’ This class includes modesty, blind charity, impulsive courage, and a species of forgiveness, as well as of trust. In this chapter I will be discussing these virtues and alluding to the problems they pose for standard views of virtue, particularly the Aristotelian theory discussed in the previous chapter. I will take modesty as my paradigm case of this type of virtue.

    MODESTY

    “My dear Watson, … I cannot agree with those who rank modesty among the virtues. To the logician all things should be seen exactly as they are, and to underestimate one's self is as much a departure from truth as to exaggerate one's own powers.” (Sherlock Holmes, from “The Greek Interpreter” by Sir Arthur Conan Doyle)

    ‘Modesty’ has at least two senses. There is the sexual sense of modesty, usually considered a womanly virtue, which primarily consists in a chaste and unassertive countenance. There is also the more usual sense that is associated with self-deprecation or an underestimation of one's selfworth. It is this latter sense that concerns me in this chapter. And the previous quotation encapsulates a good deal of what I want to say about this sense of ‘modesty.’

  • Introduction

  • Julia Driver, Dartmouth College, New Hampshire
  • Book:
    Uneasy Virtue
    Published online:
    22 July 2009
    Print publication:
    23 April 2001, pp xiii-xxii

  • Summary

    Over the past few decades, criticism of Utilitarianism, and consequentialism more generally, has become increasingly fashionable. Currently popular is the view that the moral quality of our lives is best captured by alternative theories such as virtue ethics or Kantian ethics. These views are considered superior in that they avoid classic problems of Utilitarianism: they are not as demanding of moral agents, and they do not necessarily advocate an impersonal standard for determining right action. Further, each of these theories locates what is morally important or significant as being within the agent or agency, whereas consequentialist theories are typically viewed as locating these factors externally, in the form of consequences. Thus, while a Kantian maintains that the moral worth of a person's action is determined by conscious adherence to the Categorical Imperative, the Utilitarian holds that the rightness of the action is determined by its consequences. This feature of Utilitarianism is seen as a weakness since it is taken to ‘alienate’ the agent from morality and, further, render the agent hostage to the forces of moral luck. This book, however, will seek to defend consequentialism from the encroachment of virtue ethics in both its Aristotelian and Kantian forms by, first, pointing out serious internal deficiencies with Aristotelian virtue ethics; second, illustrating some of the limitations and the very narrow scope of virtue within the Kantian system; and, third, showing that consequentialism can well accommodate virtue evaluation. These three themes will be the central themes of the book.

  • Conclusion

  • Julia Driver, Dartmouth College, New Hampshire
  • Book:
    Uneasy Virtue
    Published online:
    22 July 2009
    Print publication:
    23 April 2001, pp 109-110

  • Summary

    The purpose of this book has been to set out and defend an objective consequentialist account of moral virtue. It has not been to defend a complete account of objective consequentialist moral evaluation, though I believe such an account to be the correct one.

    In the course of arguing for this view, I have attempted to make distinctions that I also believe help to clarify crucial differences between different accounts of moral virtue. I have also tried to show that the classical account is deeply flawed – in a way, an intellectually elitist account that places enormous psychological requirements on moral virtue. Of course, the view I propose, at the other end of the spectrum, will to many people have the opposite problem of making virtue too easy and accessible – perhaps I should have called the book Easy Virtue. But this inference would be a mistake. Virtue may or may not be easy for the agent. That's the whole point behind the attempt to deflate the conflict between Aristotle and Kant. After all, for Aristotle, once the virtuous agent has the virtue, it starts looking easy too. My account simply holds that a trait that is good-producing – however acquired – is a moral virtue. It may be contingently true that these traits tend to be ones that we have to work hard to acquire and that require some effort to maintain. My view is simply that this is not a necessary feature of moral virtue.

  • 3 - Dubious Virtue Psychology

  • Julia Driver, Dartmouth College, New Hampshire
  • Book:
    Uneasy Virtue
    Published online:
    22 July 2009
    Print publication:
    23 April 2001, pp 42-62

  • Summary

    In the previous chapter we considered arguments against a particular psychological or cognitive requirement for virtue. The virtues of ignorance count against a knowledge, or correct perception, requirement for virtue. If I am correct, to have some virtues the agent need not have knowledge of morally relevant facts. There are other very specific kinds of psychological states that have been viewed as necessary to virtue throughout the historical development of virtue theory. This chapter continues the assault on an internal requirement for moral virtue. I argue that any account of virtue that defines virtue in terms of some specific sort of psychology will fail because such an account will be too narrow.

    THE VIRTUES AS CORRECTIVES

    Facts about human psychology have frequently been considered crucial in defining virtue. For example, one popular view of the virtues, which can be traced back to Aquinas and has been recently developed by Philippa Foot, is that they work to “correct” for the baser human impulses and motives (Foot 1978). The idea is that humans are naturally self-interested and motivated by considerations of selfishness, by the desire to promote their own good, and by an aversion to whatever constitutes something bad for them as individuals. This type of view is articulated by Philippa Foot in Virtues and Vices. Virtues correct both for temptations that humans typically experience and for deficiencies of motivation to do good.

  • 1 - The Aristotelian Conception of Virtue

  • Julia Driver, Dartmouth College, New Hampshire
  • Book:
    Uneasy Virtue
    Published online:
    22 July 2009
    Print publication:
    23 April 2001, pp 1-15

  • Summary

    In the recent resurgence of interest in virtue, Aristotle's theory has pride of place. He provided one of the first comprehensive theories of virtue, one that placed a great deal of emphasis on the exercise of our rational faculties and the integration of the rational with the emotional. It is an attractive theory because Aristotle focused on the issue of what it was to be a good person in developing his theory. Many recent ethicists find this a welcome relief from theories that focus on the evaluation of action. The Aristotelian view has become extremely influential. For example, Alasdair MacIntyre views the Aristotelian tradition as the one that will save ethics from aimless fragmentation (MacIntyre 1979). Rosalind Hursthouse has recently presented a neo-Aristotelian account of virtue ethics (Hursthouse 1999). John McDowell appropriates the Aristotelian idea that virtue involves correct perception of morally relevant facts (McDowell 1979). The virtuous agent recognizes what is good, “sees things as they are,” and acts accordingly. It is the “seeing things as they are” element of Aristotle's theory that has permeated virtue theory (see also Murdoch 1970, Blum 1991). And it has scarcely been challenged. One aim of this book is to challenge this condition of virtue. One of my claims, argued for in Chapter 2, is that correct perception, while important, is not necessary for virtue.

  • 5 - Virtue and the Will

  • Julia Driver, Dartmouth College, New Hampshire
  • Book:
    Uneasy Virtue
    Published online:
    22 July 2009
    Print publication:
    23 April 2001, pp 84-108

  • Summary

    The metaphysics of virtue needs to be distinguished from the epistemology. The account of what a virtue is has been outlined. However, there is still the epistemological problem of how to determine what consequences of the trait count. Suppose that we were all grossly mistaken about the benefits produced by generosity. Suppose that generosity only produced good consequences in the short term, but the long-term consequences were devastating. If generosity toward the needy in the long run produced parasites, or persons whose characters had in some way been undermined, and if generosity did this systematically, then it would not be a moral virtue. Long-term consequences count. For this reason, I think it entirely likely that we are mistaken in calling some traits virtues precisely because we fail to see the harmful effects these traits produce. Those traits with good foreseeable consequences are the ones we regard as virtues – though the judgment could be mistaken. The more we know about the world, the fewer mistakes we will make. These observations provide a great deal of intuitive support for a consequentialist theory of virtue. The fact is that when we do see that we have misjudged the consequences of a trait, we change our judgment of the trait's status as a virtue.

    Chastity may be an example of this. Chastity for women is not generally considered to be a moral virtue anymore, though it certainly used to be considered one.

  • 7 - The Subjective Experience of Intertemporal Bargaining

  • George Ainslie, Veterans Affairs Medical Center, Coatesville, Pennsylvania
  • Book:
    Breakdown of Will
    Published online:
    05 June 2012
    Print publication:
    19 March 2001, pp 105-116

  • Summary

    The hyperbolic discounting hypothesis has pushed us beyond both documented fact and common sense. Yes, the hyperbolas themselves are well-established facts, and yes, people do suffer from persistent motivational conflicts that conventional utility theory can't explain. We do talk sometimes about arguing with ourselves. Nevertheless, we experience ourselves as basically unitary; and if bundling choices into mutually dependent sets is central to the process of intending things, it has gotten amazingly little recognition.

    In common speech “personal rules” don't mean the same thing as “willpower.” They sound trivial, like guidelines for deportment – something a given person might not even have. I've applied the term to something much more central in human decision making. However, the very existence of personal rules as I've hypothesized isn't proven. So far the only evidence I've presented for them is that (1) hyperbolic discount curves predict a limited war relationship among interests, and (2) bundling choices together has been observed to increase patience.

    Even our one robust experimental finding is counterintuitive: that the valuation process is based on hyperbolic discount curves, and hence is prone to extreme instability because of a tendency for decisions to reverse simply because time has passed. It's not that we don't observe the problems that these curves predict: The human bent for self-defeating behavior has been in the forefront of every culture's awareness. This, after all, is sin, or the weakness of the flesh, or the mistaken “weighings” of options that Socrates complained of.

Page 146 of 207