Psy 416: Reasoning and Problem Solving
  Deduction: Form, logic, and logical reasoning

Erwin Segal
Associated with this topic is a Primer on Logic. Click here to see it.
Also see Suber
Homework

1.  Logical appraisal
When a person says or writes something there are many different ways in which her performance may be judged. Did she say something nice? Did she speak well? Did she articulate clearly? Could I understand what she meant to say? Has she used apt metaphors? We may take any number of different stances to her discourse. Among these is a logical stance. In this stance arguments are evaluated for their truth and validity.

We may examine the logical structure of a discourse and evaluate whether it can withstand logical analysis. We can evaluate to what extent the conclusions drawn are justified by the premises.

Logic is reasoning based on the idea that often if some statement or set of statements is true, some other possible statements must also be true, others may be true and may be false, and still others must be false. We all probably reason this way some of the time.

 For example, if you knew the following two statements to be true:
(1a) If a person does not practice, he or she will not become an accomplished pianist.
(1b) Susan took piano lessons for years, but she never practiced. you could conclude (1c) Susan is not an accomplished pianist. Go to the Primer on Logic 1  II.  A widespread AI, Cognitive Psychology, and Cognitive Science principle is that there are well-specifiable procedures which represent the way that people think. These involve applying logic type rules to a formal representation base. The study of reasoning in this case is the discovery of the form of the representation and the rules of inference that people use. The method proceeds something like this: 1. Incoming information is transformed into a symbolic representation of the implied proposition. There are certain formal ways in which propositions are logically interrelated, and conclusions derived. These are implemented by the application of rules of derivation or other principles. In information processing systems, they are the application of efficient procedures which represent algorithms or heuristics.
2. This kind of system can derive valid conclusions or evaluate arguments as to their validity.
3. Errors can occur when a) there are errors in the representations, b) derivations are not completed. c) there are errors in the rule system, d) the wrong rules are applied.
4. A problem of application is: it is not always clear how to get from premises to representations, nor for some problems, what the derivation rules are. III.  One way of solving logic problems is by applying rules of derivation directly to the symbolic forms representing the propositions. Certain forms (premises) can be transformed into other forms (conclusions).
IV. An alternative approach is based on implementing the premises in models.  Models come in different variants, lists of tokens, Venn diagrams, images of the details of the propositions described. etc. (e.g. Johnson-Laird, 1983, Mental Models, Harvard Univ. Press) 1. Model building is one way that people tend to solve (logic) problems: (a) they attempt to build a mental (or external) structural representation (=model) of the relevant content information in the premises,
(b) then interrogate the model to see whether the conclusion is already contained there.
(c) if so, conclude that the argument is valid; if not conclude that it is invalid. 2. Reasoning may fail when: (a) model does not accurately reflect premises
(b) model only incompletely represents premises
(b) models of premises are not integrated accurately--e.g. representation of earlier premises may not be incorporated when later premises are added
(c) if person is using mental models, model of premises is not remembered during conclusion evaluation
(d) interrogation is not accurately completed. 3. Problems with model theories: (a) There is no single universal structure for mental models of propositions.
(b) It is not always clear what the relevant components are.
(c) It is not obvious how to model some meanings; some meanings are very difficult to model using certain model schemata.
(d) It is not always clear how people may interrogate the model, nor is it always clear how to use the model to draw valid conclusions. IV.  Although much psychological research has been done on reasoning based on logical form, logical reasoning seems to be secondary to reasoning from content in many instances. Content reasoning may be based on previous knowledge or even innate tendencies to use certain reasoning schemas.

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