Changes

=====4.3.3.1. Analogy=====

=====4.3.3.1. Analogy=====

The classic description of analogy in the syllogistic frame comes from Aristotle, who called this form of inference by the name “paradeigma”, that is, reasoning by example or by a parallel comparison of cases.

The classic description of analogy in the syllogistic frame comes from Aristotle, who called this form of inference by the name "paradeigma", that is, reasoning by example or a parallel comparison of cases.

We have an Example (paradeigma, or analogy) when the major extreme is shown to be applicable to the middle term by means of a term similar to the third.  It must be known both that the middle applies to the third term and that the first applies to the term similar to the third.

<p>We have an Example (''paradeigma'', or analogy) when the major extreme is shown to be applicable to the middle term by means of a term similar to the third.  It must be known both that the middle applies to the third term and that the first applies to the term similar to the third.</p>

Aristotle illustrates this pattern of argument with the following sample of reasoning.  The setting is a discussion, taking place in Athens, on the issue of going to war with Thebes.  It is apparently accepted that a war between Thebes and Phocis is or was a bad thing, perhaps from the objectivity lent by non involvement or perhaps as a lesson of history.

Aristotle illustrates this pattern of argument with the following sample of reasoning.  The setting is a discussion, taking place in Athens, on the issue of going to war with Thebes.  It is apparently accepted that a war between Thebes and Phocis is or was a bad thing, perhaps from the objectivity lent by non involvement or perhaps as a lesson of history.

E.g., let A be "bad", B "to make war on neighbors", C "Athens against Thebes", and D "Thebes against Phocis".  Then if we require to prove that war against Thebes is bad, we must be satisfied that war against neighbors is bad.  Evidence of this can be drawn from similar examples, e.g., that war by Thebes against Phocis is bad.  Then since war against neighbors is bad, and war against Thebes is against neighbors, it is evident that war against Thebes is bad. (Aristotle, Prior Analytics, 2.24)

<p>E.g., let A be "bad", B "to make war on neighbors", C "Athens against Thebes", and D "Thebes against Phocis".  Then if we require to prove that war against Thebes is bad, we must be satisfied that war against neighbors is bad.  Evidence of this can be drawn from similar examples, e.g., that war by Thebes against Phocis is bad.  Then since war against neighbors is bad, and war against Thebes is against neighbors, it is evident that war against Thebes is bad.</p>

| align="right" | (Aristotle, ''Prior Analytics'', 2.24)

We may analyze this argument as follows.  First, a Rule is induced from the consideration of a similar Case and a relevant Fact.

We may analyze this argument as follows.  First, a Rule is induced from the consideration of a similar Case and a relevant Fact.

D => B, "Thebes vs Phocis is war against neighbors". (Case)

 

| width="20% | <math>D \Rightarrow B,</math>

D => A, "Thebes vs Phocis is bad". (Fact)

| width="60% | "Thebes vs Phocis is war against neighbors".

 

| width="20% | (Case)

B => A, "War against neighbors is bad". (Rule)

| <math>D \Rightarrow A,</math>

| "Thebes vs Phocis is bad".

| (Fact)

| <math>B \Rightarrow A,</math>

| "War against neighbors is bad".

| (Rule)

Next, the Fact to be proved is deduced from the application of this Rule to the present Case.

Next, the Fact to be proved is deduced from the application of this Rule to the present Case.

C => B, "Athens vs Thebes is war against neighbors". (Case)

 

| width="20% | <math>C \Rightarrow B,</math>

B => A, "War against neighbors is bad". (Rule)

| width="60% | "Athens vs Thebes is war against neighbors".

 

| width="20% | (Case)

C => A, "Athens vs Thebes is bad". (Fact)

| <math>B \Rightarrow A,</math>

| "War against neighbors is bad".

| (Rule)

| <math>C \Rightarrow A,</math>

| "Athens vs Thebes is bad".

| (Fact)

In practice, of course, it would probably take a mass of comparable cases to establish a rule.  As far as the logical structure goes, however, this quantitative confirmation only amounts to "gilding the lily".  Perfectly valid rules can be guessed on the first try, abstracted from a single experience or adopted vicariously with no personal experience.  Numerical factors only modify the degree of confidence and the strength of habit that govern the application of previously learned rules.

In practice, of course, it would probably take a mass of comparable cases to establish a rule.  As far as the logical structure goes, however, this quantitative confirmation only amounts to "gilding the lily".  Perfectly valid rules can be guessed on the first try, abstracted from a single experience or adopted vicariously with no personal experience.  Numerical factors only modify the degree of confidence and the strength of habit that govern the application of previously learned rules.

=====4.3.3.2. Inquiry=====

=====4.3.3.2. Inquiry=====