So I am pleased to find Allen MacNeill's descriptions and analysis of the functions of analogy in logical reasoning. I'm also cheered that he's been working on these for 25 years, since it suggests there may be good reason for my not having yet "gotten it."
I won't go into detail about MacNeill's descriptions, but he goes over seven areas at a nicely specific level:
- Validity, confidence, and logical argument
- Transduction relates a single premise to a single conclusion, and is therefore the weakest form of logical validation.
- Induction validates generalizations only via repetition of similar cases, the validity of which is strengthened by repeated transduction of similar cases.
- Deduction validates individual cases based on generalizations, but is limited by the induction required to formulate such generalizations and by the transduction necessary to relate individual cases to each other and to the generalizations within which they are subsumed.
- Abduction validates new generalizations via analogy between the new generalization and an already validated generalization; however, it too is limited by the formal limitations of transduction, in this case in the formulation of new generalizations.
- Consilience validates a new generalization by showing via analogy that several already validated generalizations together validate the new generalization; once again, consilience is limited by the formal limitations of transduction, in this case in the validation of new generalizations via inferred analogies between existing generalizations.
- Taken together, these five forms of logical reasoning (call them "TIDAC" for short) represent five different but related means of validating statements, listed in order of increasing confidence.
- The validity of all forms of argument are therefore ultimately limited by the same thing: the logical limitations of transduction (i.e. argument by analogy).
- Therefore, there is (and can be) no ultimate certainty in any description or analysis of nature insofar as such descriptions or analyses are based on transduction, induction, deduction, abduction, and/or consilience.
- All we have (and can ever have) is relative degrees of confidence, based on repeated observations of similar objects and processes.
- Therefore, we can be most confident about those generalizations for which we have the most evidence.
- Based on the foregoing analysis, generalizations formulated via simple analogy (transduction) are the weakest and generalizations formulated via consilience are the strongest.