Psy 416: Reasoning and Problem Solving

Submit homeworks via email to segal@acsu.buffalo.edu

Spring 2003--Due Wednesday January 22
Homework 1. Read excerpt from Plato's Meno . Answer the following 2 interrelated questions 
1. What does someone need to know in order to be able to double a square?
2. Do you agree with Socrates that the slaveboy innately knew how to double a square, but was unaware of that innate knowledge ? Argue for your position. (consider what the boy needed to know before the episode began)

Due Wednesday February 5, 2003
Homework 2. Answer Problems 1, 2, and 4 (concerning Euclid's Algorithm) on Page 16 in the Graham chapter on reserve.

Due Monday March 3, 2003.
Homework 3.

I
Use Venn diagrams to show whether the following syllogism is valid.
All A are B
Some B are C
Some A are C

1. P is equivalent to PÚ (P&Q), use equivalence symbol and show that it is always true
i.e., show that:  Pº (PÚ (P&Q))
2. (P É Q) º (~PÚ Q)
3. Modus Ponens is true. Can be done by showing that if AÉ B and A, are both true B must be true.

This can be done by showing that ((A É B) & A) É B is a tautology. This shows that B follows from AÉ B and A.
4. If the antecedent of an 'if then' sentence is false, does it follows that the consequent sentence is false? From A É B and ~A, can you derive ~B?

        III
Which conclusions follow from these premises? Why?

                                                  Conclusions
                                    All A      Some A     No A     Some A      None of
                                    are C       are C         is C     are not C     these
                                            (for other possibilities reverse the A and C)
1. All A are B
    Some B are C

2. All A are B
    Some C are not B

3. All A are B
    No C is B

4. Some A are B
    No B is C

5. All B are A
    All C are B

____________________________________________
 
Homework 2. (Due Thursday Sept 19, 5 pm.)
1. Explain the Differences between Wertheimer's A problems and B problems identified in the reading on Gestalt on reserve.
2. Roughly outline how some of the concepts of  connectionism (many simultaneous excitatory and inhibitory connections) may be used to explain how anagrams are solved. If  you are at an impasse, show how these processes can be used to explain how one of the examples on the " Notes to Connectionism " (linked to the Association Page link to the syllabus)  may work. Homework 4. Due Tuesday October 28, 5 pm.
I am not able to meet class on Friday Oct 25.
Read Chapters 7 "Mental Chronometry" and 9 "Question Answering" and my notes linked to the syllabus.

1. By combining ideas of semantic memory relations (concepts are structurally interlinked according to some principles of meaning) and mental chronometry (different mental processes take time to execute), describe a representation and a procedure that could explain why you might decide that "Canaries fly" as fast as "Canaries are yellow", and that these are decided faster than "Canaries have bones." 

Homework 5. Developmental aand Schema questions. Due Friday November 15 at 5 pm.
1. How does Vygotsky's concept of "Zone of Proximal Development" or Chi's idea that children are universal novices contrast with Piaget's stage analysis of cognitive development?
2. Use an example to help explain how schemas can and do affect understanding and interpretation.