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Chapter 9: Sections 9.1, 9.4-9.6

9.1 Analogy and Legal Reasoning

9.4 Statistical Reasoning

9.5 Hypothetical/Scientific Reasoning

Notes for Chapter 9

The following notes highlight concepts you should understand from the assigned readings. They are neither intended to replace the lectures and text, nor to substitute for a reading of the text. Lectures will add to and supplement material given here. In order to do well in this class, it is recommended that you review these notes to identify main ideas after having attended class.

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Prior Resource Listings

  • The Philosophy of Logic: this page contains good background information and plenty of links for those interested in exploring history and various approaches to theoretical logic. There is also an especially good page entitled Defining Necessity and Contingency that describes the difference between necessary and sufficient conditions.

  • Want to take a look at what logicians are thinking about? Here's a link to Analysis Web where you'll find professional logicians discussing their craft.

  • The Critical Thinking Site at Longview Community College: this site has long been an excellent resource for beginners and advanced students of logic. I advise you to explore this site if you're looking for more explanations of basic concepts.

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    Chapter 9: Section 9.1

    Analogy

    Analogical reasoning is the most common of all the reasoning processes used in rational argument.(486)

    Some critical components of analogical reasoning:

    • "depends on a comparison of instances"(486)
    • it is "closely related" to the process of generalization(486)
    • "the items that are compared are called analogates"(486)
      1. primary analogates: known earlier exemplars of a given thing or condition that inspire us to analogize about similar items/events in the future.
      2. secondary analogate: an item or condition that one tries to judge/predict likely outcomes for, based on prior experience with similar items/conditions.

    Hurley identifies six criteria that "are useful for evaluating most arguments from analogy."(486-88)

    1. relevance of the similarities shared by the primary and secondary analogates: the process of choosing and comparing relevant criteria for making an accurate assessment
    2. number of similarities: Events/items that are similar in nature are easily compared analogously. Thus the more relevant similarities, the better the comparison.
    3. nature and degree of disanalogy: the process of assessing differences between two objects/events under comparison. The type and magnitude of difference between two things negatively impacts our ability to make accurate assessments.
    4. number of primary analogates: Primary analogates are a collection of similar objects or events being used as exemplars for new comparisons. Thus, the more experience one has with a particular object/event, the better he/she is able to make accurate analogous judgments.
    5. the diversity among primary analogates: Primary analogates are best used for comparison purposes when the number of similarities between each object/event is high. Objects/events that are significantly different do not help us to make accurate general predictions.
    6. the specificity of the conclusion: the more detailed the prediction made in the conclusion, the weaker the chance of accuracy in analogous assessment.

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    Legal Reasoning

    Lawyers rely heavily on analogical arguments to support their claims. Much of the time spent in legal research is devoted to finding similar cases/rulings that will assist one in crafting a favorable argument.(488)

    Common Law versus Statutes

    • Common Law - "judge-made law"(489); based on rulings made by judges; particular to general case

    • Statutes: laws made by legislative bodies "codified in books that are periodically revised"(489); the laws are usually written in "general language" so "precedent is required to determine how the statutes should be interpreted and applied."(489) Application process is general ideal to a particular instance; thus, interpretation plays a large in the final ruling process.

      • All cases that are being tried under a new law (i.e., first-time application of a new statute) are precedent-setting cases.

      • A precedent-setting case is said to be "on point" if the case to which it is currently being applied resembles it "in virtually all important details."(490)

      • If the nature and degree of disanalogy is quite large, then the precedent may/may not apply.

    • Cases "for which there is no clear precedent ...are called cases of first impression."(492)

      • Moral reasoning and analogies are the core material used in making a ruling.

      • Reasoning process: a series of "analogies followed by disanalogies and counteranalogies."(492)

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    Section 9.4

    These notes are minimal summaries of what is presented in the above referenced section.

    Samples:

    • Biased samples are not representative of the population to which they refer.(548)
    • Random sampling is also critical, especially for human populations under study. The criteria for randomness is met "if and only if every member of the population has an equal chance of being selected."(546)
    • The size of the sample is also incredibly important when we are trying to determine the sampling error (see page 548 for complete definition). Briefly the sampling error is measure of how our polling data reflects the actual behavior of the population under study. There is a chart on p.548 that explains how sample size and sample error are related.
    • Last, psychological factors will also play an important role in cases where our "population consists of human beings."(549)
      • question-type(549)
      • interaction between surveyor and respondent(549)
      • motivation for conducting the study(552)

    Average: multiple meanings

    • mean: arithmetical average
    • median: "middle point when the data are arranged in ascending order."(551)
    • mode: "value that occurs with the greatest frequency."(551)
    • The type of situation at hand determines which kind of average will be most useful. See pages 551-552.
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    Dispersion: the "spread" of a data set

    • range: "difference between the smallest and largest numbers."(553)
    • variance: measure of "how far the data vary or deviate from the mean."(553)
    • standard deviation: "square root of the variance"(553)
    • The bell curve, or normal probability distribution, represents various sets of data in which the mean, median and mode all have identical values.(556)
    • Dispersion affects our interpretation of data results because it provides further detail concerning the relationship of the mean to the data set. For further clarification see the discussion on pages 556-557.

    Graphs and Pictograms:

    • Pictures are easily used to misrepresent data.
    • Graphs: should have both horizontal and vertical axes scaled.(558)
    • Pictograms are even more susceptible to data misrepresentation.(560)

    Percentages:

    • Always ask yourself what is the given percentage a percentage of?(561)
    • One method for manipulating data is to switch numbers used for comparison and then to calculate percentages based on different data. Comparisons of this sort of data are misleading.(561)
    • Another method used to misrepresent data is the use of two different bases to calculate percentages.(562)
    • We cannot add percentages as we do cardinal numbers.(562)
    • We can also suppress evidence when we ignore relevant factors in our calculation of percentages.(562)

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    9.5 Hypothetical/Scientific Reasoning

    Hypotheses serve as experimental tools to prove/disprove a claim that is not amenable to direct observation.(567)  For our purposes we will be discussing hypothetical reasoning as it relates to philosophical and scientific inquiry.

    Three critical points about hypotheses:

    1. "A hypothesis is not derived from the evidence to which it pertains but rather is added to the evidence by the investigator."(569)

    2. "A hypothesis directs the search for evidence."(569)

    3. You have to have multiple forms of support to prove a hypothesis true. In other words, proving one implication true is not enough to prove an entire hypothesis.(569)

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