Deductive Reasoning

Are the following syllogism valid? A syllogism is valid if the conclusion follows from the premises All soldiers are sadistic Some soldiers are women therefore, some women are sadistic Every alive person has a heart Every person in this class has a heart Therefore, every person in this class is alive What is belief bias (?) (see Reisberg p. 417)

Deduction: Normative vs. Descriptive Models Normative models (rules of logic). They specify - what conclusions can be drawn given a set of premises. - what evidence is needed for certain conclusions. - it is called formal logic because it deals with the syntax, not the content of the reasoning Descriptive models describe how people actually reason.

Rules of logic: Modus ponens If p, then q p(premise) Therefore, q If Saddam has WMD, we’ll invade Irak Saddam has WMD.(premise) Therefore, we’ll invade Irak Note: if he doesn’t have WMD, we’ll invade anyhow This later conclusion follows formal logic, but violates pragmatic principles. In English we interpret the rule to be ‘if and only if’ It is unfair to say people are being irrational (why should the language of logic take precedence over conventional language?)

Rules of logic: Modus tollens If p, then q not q Therefore, not p If premise “p” is true then premise q is also true. Premise q is false Therefore premise p must be false.

(1) If horses drank at the waterhole, we would see their tracks. We see no tracks Therefore the horses did not drink at the waterhole. (2) If horses drank at the waterhole, we would see horse tracks. We see horse tracks Therefore the horses drank at the waterhole. Are these arguments true? Argument (1) is valid, but argument (2) is invalid.

The Wason Card Selection Task AF67 If a card has a vowel on one side, it has an even number on the other side. Which cards should be turned over to determined whether this rule is being followed?

AF67 The correct answer: Most people select A and 6 to test the ‘if and only if’ Tests Modus Ponens Tests Modus Tollens

Another version of the Wason card selection task: 25 yrs old Rule: If a person is drinking beer, she has to be 21 or older. Each card has the drink on one side, and the person’s age on the other side. Which cards should you check? 16 yrs old Modus Tollens This is very easy, but why?!

25 yrs old 16 yrs old Modus Tollens This is very easy, but why?! - familiar - pragmatic rules (cause-effect rule, permission rule, etc) - social nature of the task (social reasoning) All of these possibilities favor concrete rules in which the content does matter, rather than the abstract rules of formal logic

Case-based Reasoning people don’t usually use abstract logical rules, but instead reason by comparing new situations to specific cases they’ve dealt with in the past This still leaves several alternatives: - familiarity - pragmatic rules - social reasoning.

Against mere familiarity Rule: Anyone consuming Coca-Cola on these premises must be at least 100 years old. 102 yrs old 56 yrs old People perform well on this version of the task even though they aren’t familiar with rule. But the rule is worded so that it evokes the permissions schema.

Pragmatic Reasoning Schemas - Schemas are related to our past experiences, and - they represent a complex set of expectations about an event (e.g. the “going to a restaurant” schema) Pragmatic Reasoning Schemas: are a particular kind of schema that represent information about goals and event relationships. For example, the beer and age example brings to mind a pragmatic reasoning schema having to do with permission “If one wishes to take a certain action, then one must have permission.” “If one has permission to take a certain action, then one may take the action.” these rules are only applied successfully in situations of permission (they are not abstract rules of reasoning)..

Confirmation bias. Tendency to seek, use and remember evidence that confirms our preconceptions - You are told you are bad at certain task, - you look for confirmation in your memory. This provides a second source of confirmation, which increases the bias. This leads to Belief Perseverance