## Thursday, October 07, 2010

### Forms of Reasoning in Factual Inference

Globular Star Cluster NGC 6934 Credit: NASA, ESA, Hubble Space Telescope

Question: How many kinds of logical processes are involved in factual inference?

Answer: Even if one ignores the reasoning that is involved in processes such as telling stories and developing scenarios -- or the reasoning that is or may be involved in matters such as "simply" classifying material such as "legal source material" -- or the reasoning that is involved in the imaginative reconstruction of meaning -- or the logical operations that are involved in "tacit" mental operations of the brain and in subconscious signal processing by human sensory organs -- or the reasoning that is used in synthetic ("holistic") thinking -- quite a few modes of reasoning, or argument, seem to be in play in factual inference, including the following:

Deduction
classic:

if you have man, then there is mortality
(you have Socrates and) Socrates is a man
therefore: there is mortality

modern form:

if a and b, then c
there is a
there is b
therefore: c

if a or b, then c
there is not-a
there is b
therefore: c

if a or b, then c
there is not-a
there is not-b
therefore: c or not-c

if not-a and not-b, then not-c
there is not-a
there is not-b
therefore: not-c

Induction
if X has property a with relative frequency .9 in n instances of X, then X (all instances of X) has property a with a relative frequency of ca. .9

if X1, X2, … X20 have property a with a relative frequency of .9, then there is a ca. .9 probability that X21 has the property a

Analogy
There are entities X and Y. There is the property a.

If water is added to X, X acquires the property a.
Y is similar (in relevant respects) to X.
If water is added to Y, Y (probably) acquires property a.

If water is added to X, X acquires property a.
Y is similar (in relevant respects) to X.
If water is is added to Y, Y (probably) acquires a property similar to property a.

If water is added to X, X acquires the property a.
Liquid nitrogen is similar (in relevant respects) to water.
If liquid nitrogen is added to X, X (probably) acquires the property a (or a property similar to a).

Abduction & Abduction-Retroduction
The existence of M is surprising.
If E were true, it would explain M.
Therefore: E may be true.

The existence of M is surprising.
If E were true, it would best explain M.
Therefore: E is most probably true.

The existence of M is surprising.
If E were true it would explain M.
If E is true, the chances of (the existence or occurrence of) X, Y, and Z are high.
X, Y, and Z exist.
Therefore: there is some (perceptible positive) probability E is true.

Subsumption & Classification
If there is an x, then y
m is an x
Therefore: y

If there is an x, then y
m has all of the properties of x
Therefore: y

If there is an x, then y
m has many of the properties of x
Therefore: there is (probably) an x
Therefore: there is (probably) a y

If there is an x, then y
m has the properties of x to some degree
Therefore: there is to some degree an x
Therefore: there is to some degree a y

If there is an x, then y
m is similar to x
Therefore: there is (probably) an x
Therefore: there is (probably) a y

Postscript: The above catalogue is, I trust, somewhat more meaningful than the following Borgesian classification of animals:

1. fat animals
2. rational animals
3. animals with four feet
4. animals with four feet and two tails
5. animals with brown hair