Quine and Ullian, C7 and C8

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Chapter 7: Induction

• Quine and Ullian claim induction is based upon a kind of analogy.
• Quine and Ullian consider induction and review Goodman's new problem of induction.
• Goodman's problem of induction:
  • Let grue be the property of being green until 2050, and then being blue.
  • All emeralds seen before now are green.
  • Two hypotheses are now supported by all the evidence we have:
    1. All emeralds are green
    2. All emeralds are grue
  • Inductive evidence supports both standard hypotheses but also these strange ones.
• Other problems of induction:
  • Every moment of my life has the property of being before 2005. This is consistent with the hypothesis that all moments of my life are before 2005.
  • Every moment of my life was followed by another moment. This is consistent with the hypothesis that I will live forever.
• Goodman claimed the problem with the property grue is that it is not "projectible." Quine and Ullian agree.
• What makes some properties projectible? Q&U believe simplicity may have something to do with it, but since they think simplicity is subjective they cannot rest on this.
• Their solution is that they don't know what makes a property projectible, but they claim evolution led us to focus in our reasoning on projectible properties.

An Aside: Simplicity and Projectibility

• Recall our theoretical virtues, which come in rank order:
  1. Predictive power
  2. Coherence
  3. Simplicity
• I have argued that simplicity is actually an objective property (when the measure used is Kolmogorov complexity).
• But then, we can drop the notion of "projectibility," and just note that the theory that emeralds are grue is more complex than the theory that they are green. This is because it makes reference not only to green, but to blue, and to a date.
• Grue is a perfectly acceptable property to ascribe, but as a theory there are simpler alternatives.
• What about my sudden death or immortality? These are also decent hypotheses, if it were not for the fact that we have no vast numbers of other examples of human lifespans, all of which are finite. When they do end, we find it is for various reasons, none of which is that a certain date has been reached.