• Fodor (2002) Reply to Beaman. Cognition 83, 221.

• Thoughts are compositional representations. See The language of thought hypothesis.

• Modus ponens. P→Q. P. Therefore, Q. demo

• [Required] Chapter 2. Thagard. (2005). Mind: Introduction to cognitive science. 2nd edition. MIT Press.

• Evolutionary psychology - We have a "cheater detection module". In the drinking problem, violators of the rule are cheaters who do not have to pay the cost. This possibility of cheaters engages the module.

• Evolutionary psychology - We have a "cheater detection module". In the drinking problem, violators of the rule are cheaters who do not have to pay the cost.

Comments

• Rules for manipulating models?
• Complexity of models varies with difficulty of problem?
• Applicable only when mental imagery is used?

Objection #4: The theory of mental models provide a better alternative

• Maybe they use the correct rules but apply them wrongly.

Theory: Reasoning = construction of mental proofs

• Knowledge of logic helps explain:
  • Our problem-solving abilities - minimal logic seems necessary for survival
  • Our knowledge of logical connections

Reasoning as mental proof

• Chapter 2. Thagard. (2005). Mind: Introduction to cognitive science. 2nd edition. MIT Press.

See also: Buller DJ. (2005). Adapting Minds : Evolutionary Psychology and the Persistent Quest for Human Nature. Bradford Books, New York.

Comments

Three types of rules:

1. Formal rules
2. Content rules
3. Mental models

• Given a statement, construct a mental model of the situation described by the statement.
• Deduction: Check whether a description is true of the model. If so, then the description is a logical consequence of the statement.
• A visual example:

@A fork is to the left of a spoon. A knife is to the right of the spoon.@

How is the fork related to the knife?

Could do this with logic using assymetry of left and right and transitivity of left.

But it's much easier to do it with a spatial mental model:

fork --- spoon ---- knife

• Chapter 2. Thagard. (2005). Mind: Introductin to cognitive science. 2nd edition. MIT Press.

• Chapter 2. Thagard. (2005). Mind: Introductin to cognitive science 2nd edition. MIT Press.

• Chapter 2. Thagard. (2005). [http://library.hku.hk/record=b3192310|Mind: Introductin to cognitive science]] 2nd edition. MIT Press.

• Reply #2: The logical form of the rules are different. See Jerry Fodor. (2000). Why we are so good at catching cheaters. Cognition. Apr 14; 75(1):29-32.

• People do poorly at the Wason's selection task but they do well at a similar task with the same logical structure.

• Conjunction fallacy, base rate fallacy

• Reply #1: But surely it can't be all general heuristics?
• Reply #2: See Jerry Fodor. (2000). Why we are so good at catching cheaters. Cognition. Apr 14; 75(1):29-32.

@Data that appear to exhibit a 'cheater detection' effect on performance in the Wason Selection task are widely interpreted as implying that deontic reasoning is effected by a domain specific, cognitive module. The 'cheater detection module' is said to offer a clear example of an effect of evolutionary selection on human cognitive architecture. This interpretation depends critically on assuming that deontic conditionals and their indicative controls are identical in structure; hence that the asymmetries in S's performance must be effects of content variables. I argue that this assumption is untrue and that structural features of deontic conditionals predict the 'cheater detection' data without assumptions about either the architecture or the history of cognition. According to this analysis, the putative cheater detection effect on the Wason task is actually a materials artifact.@

@1. It is raining and it is sunny.
2. It is raining or it is sunny.
3. It is raining.@

@4. Joe believes that Po speaks Cantonese.
5. Everything Joe believes is true.
6. It is true that Po speaks Cantonese.@

• People do poorly at the Wason's selection task but they do well at a similar real-time task with the same logical structure.
• Evolutionary psychology - We have a "cheater detection module".

• Still relies on compositional representations.

It is raining or it is sunny.\\

• Knowledge of logic helps explain: survival and problem-solving, intuitions about logical connections.

It is raining.@@@

• Knowledge of logic helps explain:
  • Survival and problem-solving
  • Intuitions about logical connections.

@@@It is raining and it is sunny.
It is raining or it is sunny. It is raining. @@@ @Joe believes that Po speaks Cantonese.
Everything Joe believes is true.
It is true that Po speaks Cantonese.@

• But surely it can't be all general heuristics?

@Our neural circuits were designed by natural selection to solve problems that our ancestors faced during our species' evolutionary history.@

• http://www.psych.ucsb.edu/research/cep/primer.html

• Rips, L. (1994). The Psychology of Proof: Deductive Reasoning in Human Thinking. Cambridge, Massachusetts: MIT Press.

• How we actually reason vs. how we ought to reason.

• Reasoning as the construction of mental proofs.
• Thoughts are compositional representations. See The language of thought hypothesis?.
• Mental processes are structure-sensitive rules operating on those representations.
• Mental proofs = step-by-step application of logical rules to thoughts.

• Logic only explains deductive reasoning.
• We also need probability theory, Bayesian principles

• P.N. Johnson-Laird, Vittorio Girotto, and Paolo Legrenzi. 1998. Mental models: a gentle guide for outsiders.

• Maybe they use the wrong logical principle.
• Maybe they use the correct rules but mis-apply them.

• Do we have modus tollens? P→Q. ¬Q. Therefore, ¬P.
  • Or do we rely on: Assume P. Therefore Q. Contradiction. Therefore ¬P.

• Wrong logical principle? Application errors?
• Modus tollens: P→Q. &notlQ. Therefore, ¬P.

Objection #2: Logic cannot explain inductive reasoning

Objection #3: People use domain-specific heuristics rather than abstract logic

Objection #4: The theory of mental models provide a better alternative

@All kakas are dadas.
Peter is a dada.
Therefore Peter is a kaka.@

Objection #1: People often do not reason logically

@All train-spotters wear anoraks.
Martin is a wearing an anorak.
Therefore Martin is a train-spotter.@

• Wrong logical principle? Interference effects?

• Wason's selection task

• Add probability theory, Bayesian principles

• These rules are given by some of the principles of formal logic?

Objection #1: Logic cannot explain inductive reasoning

• Add probability theory, Bayesian principles
• Reply: People do not use principles of probability
  • Conjunction fallacy, base rate fallacy

Objection #2: People use domain-specific heuristics rather than abstract logic

• Wason's selection task
• Evolutionary psychology

Objection #3: The theory of mental models provide a better alternative

• Joe believes that Po speaks Cantonese.
  Everything Joe believes is true.\\

• Joe believes that Po speaks Cantonese.//

Everything Joe believes is true.// It is true that Po speaks Cantonese.

• Truth-conditions and meaning
• Entailment intuitions.
  • Joe believes that Po speaks Cantonese. Everything Joe believes is true. It is true that Po speaks Cantonese.

• Logic in AI - LISP, Prolog

• Modus ponens. P→Q. P. Therefore, Q.
• Logic in AI

How is logic related to reasoning?

• Do we have innate knowledge of logic?
• Does knowledge of logic explain reasoning?

@Logic, then, comprises the science of reasoning, as well as an art, founded on that science. - J.S.Mill@

Natural language and formal logic

What about inductive reasoning?

• Probability in inductive reasoning.

• Reasoning to be explained by compositional representations and structure-sensitive rules operating on those representations.

Formal logic and mental logic

Readings

• Chapter 2. Thagard. (1996). Mind: Introductin to cognitive science MIT Press.

Background

• The language of thought hypothesis?

category.mind