## 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

## Monday, October 04, 2010

### Hegel on Wall Street -- or in Left Field?

It's nice to see that the New York Times is publishing serious philosophical stuff -- see J.M. Bernstein Hegel on Wall Street NYTimes (Oct. 3, 2010) -- but methinks Hegelian ethics and politics -- like Hegelian metaphysics -- just will not fly. True, for some purposes (e.g., tort law) human beings perhaps "intend" more than the subjective intentions they have in their heads when they act. But unless omniscience and omnipotence are ascribed to human actors, human beings do not "intend," "want," or "affirm" all of the consequences precipitated by their actions. Hegelian theory offers no principled basis for drawing the line between those consequences of human actions that may be attributed to human actors and those consequences that are not properly viewed as having been chosen by an individual actor. Hegel's notion of "tacit will" may be a majestic conceptual or philosophical effort -- but it is in the end a failure because it merely restates the problem of ascription and responsibility instead of solving it. (In fairness to Hegel: Perhaps this is the fate of all philosophical analyses of individual responsibility.)

P.S. I grant that this post has little to do with the law of evidence. Or?

&&&

The dynamic evidence page

It's here: the law of evidence on Spindle Law. See also this post and this post.