Abduction

Discovery Deduction Induction Abduction Transformation Problem-solving Diagnose Language Prediction Metacognition



Mill's five methods for causal relationships

Mill's offers five methods for determining cause and effect.  These methods allow us to determine which precondition out of many is the probable cause of the effect in this case.  These methods do not result in general cause and effect relationships, that may be obtained through inductive generalization.

Inference                                                                      Method

  1. Probable Cause relationship                          Agreement
  2. Probable Cause relationship                          Difference
  3. Probable Cause relationship                         Joint Method
  4. Probable Cause relationship                         Residues
  5. Probable Cause relationship                         Concomitant Variation

  ...more...

Six types of inference

 

Peirce has offered us six types of inference from abductive methods and he gives examples of each plus a description, but I haven’t  figured out the methods yet.

 

Inference                                          Method

Omen/hunch

Symptom

Metaphor/analogy

Clue

Diagnosis/scenario

Explanation

 

 

 

Almost all of the deductive methods may be reversed and used for abductive argument or inference provided the answer is possible (i.e., plausible) rather than certain. For example:

Name Rule
Modus Ponens p > q, p; therefore q
Modus Tollens p > q, -q; therefore -p
Chain p > q, q > r; therefore p > r
Disjunctive1 p v q, p; therefore -q
Disjunctive2 p v q, q; therefore -p
Addition1 p; therefore p v q
Addition2 q; therefore p v q
 Conjunctive1   -(p & q), p; therefore -q
 Conjunctive2  -(p & q), q; therefore -p
Simplification1 (p & q); therefore p
Simplification2 (p & q); therefore q
Adjunction p, q; therefore p & q
Reductio1 p > -p; therefore -p
Reductio2 p > (q & -q); therefore -p
Complex constructive p > q, r > s, p v r; therefore q v s
Complex destructive p > q, r > s, -q v -s; therefore -p v -r
Simple constructive p > q, r > q, p v r; therefore q
Simple destructive p > q, p > r, -q v -r; therefore -p


Type Name Method
Abduction Modus Ponens p > q, q; therefore possibly p
Abduction Modus Tollens p > q, -p; therefore possibly -q
Abduction Chain p > q, q > r; therefore r > possibly p
Abduction Disjunctive 1 p v q, q; therefore possibly -p
Abduction Disjunctive 2 p v q, p; therefore possibly -q
Abduction Addition 1 p v q; therefore possibly p
Abduction Addition 2 p v q ; therefore possibly q
Abduction Conjunctive 1 -(p & q), -q; therefore possibly p
Abduction Conjunctive 2 -(p & q), -p; therefore possibly q
Abduction Simplification 1 p; therefore possibly (p & q)
Abduction Simplification 2 q; therefore possibly (p & q)
Abduction Adjunction No abductive equivalent
Abduction Reductio 1 unknown argument
Abduction Reductio 2 unknown argument
Abduction Complex constructive p > q, r > s, q v s; therefore possibly p v r
Abduction Complex destructive p > q, r > s, -p v -r; therefore possibly -q v -s
Abduction Simple constructive p > q, r > q, q; therefore possibly p v r
Abduction Simple destructive p > q, p > r, -p; therefore possibly -q v -r

These have not been tested for abductive validity yet, so use with caution.