The purpose of this assignment is to warm up for the final exam. It is worth only 2% of your course grade and is not particularly difficult. The intent is to get you to reexamine (or discover for the first time) some of the course material that may appear on the final.

Unlike the first homework assignment where you answer with essays, this assignment consists of multiple choice problems, because the final might have them as well. You should get accustomed to how awful they may be.

Please work in pairs and turn in only one hard copy, with both students' names. Simply print this page and circle the best answer for each problem. Correct answers are worth 5 points and incorrect answers are worth -1 point.

1. What is Karl Popper's best known contribution to the Philosophy of Science?
   1. A framework for scientific discourse emphasizing empiricism, testimony, and deduction
   2. His solution to the demarcation problem
   3. His demonstration that induction cannot be logically justified
   4. His view of science as a problem-solving enterprise
   5. None of the above
2. Why is "sensitivity to initial conditions" not sufficient to describe Chaos?
   1. Fractals may be insensitive to initial conditions
   2. Non-chaotic systems can also be sensitive to initial conditions
   3. Sensitivity to initial conditions is implied by dense periodic orbits
   4. All of the above
   5. None of the above
3. What is the 200th element of the sequence defined by the orbit x → 2^0.03125x starting at 1.0, and rounded to five places after the decimal point? (Note: 1.0 is the first point in the sequence, not the zeroth).
   1. 72.88247
   2. 74.47839
   3. 76.10926
   4. We do not have enough computing power on the planet to determine this
   5. It is impossible, in principle, to predict
4. What is the 500th element of the sequence defined by the orbit (x,y) → (x²-y²-1.202370, 2xy-0.124405) starting at (0, 0), rounded to five significant figures? (Note: (0,0) is the first point in the sequence, not the zeroth).
   1. (0.17880, 0.091636)
   2. (-1.17880, -0.091636)
   3. (0, 0)
   4. We do not have enough computing power on the planet to determine this to the desired accuracy
   5. It is impossible, in principle, to predict
5. Which of the following best describes the "Butterfly Effect"?
   1. The Lorenz Attractor
   2. The flap of a butterfly's wing in one part of the world can cause a hurricane in another part of the world
   3. The weather is unpredictable
   4. In many systems, we can never pinpoint the one cause of any event; a myriad of tiny events all contribute
   5. None of the above
6. Which is the best argument against emergentism, out of the following?
   1. What else could there be but the parts that make up the whole?
   2. Quantum theory shows that emergence is an illusion
   3. The hard problem of consciousness
   4. The isomer example of Schrödinger doesn't count because dark matter and dark energy show that particles do not necessarily define the whole
   5. No one has yet found an system that cannot be described reductionistically
7. How would you characterize this fractal?

   

   1. It is made of 2 copies of itself each scaled by a factor of 1/2
   2. It is made of 4 copies of itself each scaled by a factor of 1/sqrt(2)
   3. It is made of 6 copies of itself each scaled by a factor of sqrt(3)/6
   4. It is not a fractal because it is not self-similar at all
   5. None of the above
8. Which of the following sentences cannot be produced by the subset-of-English grammar in the course notes?
   1. her fast new doctor that threw a toy above alan jumped
   2. the heavy fast blue rat knew she
   3. the dog swam around grace
   4. she handed the blue girl that believed a doctor hit she to a toy
   5. donald liked her new rat
9. How do we encode the statement "All true statements are provable but the queen's daughter is a good student" in logical notation? (Here Gx means x is a good student):
   1. ∀s.(s ⊃ Ps) ∧ ℩ p. Gpq
   2. ∃s.(s ⊃ Ps) ∧ ℩ p. G(Dqp)
   3. ∀s.(s ⊃ Ps) ∧ ℩ p. G(Dpq)
   4. ∀s.(s ⊃ Ps) ∧ ℩ p. Dpq ∨ Gp
   5. None of the above
10. How do we encode the statement "Someday it will not be possible for green ideas to sleep" in logical notation?
    1. ~◊∃i.F(Gi∧Si)
    2. F~◊∀i.Gi⊃Si
    3. ~F◊∃i.Gi∧Si
    4. F~◊∃i.Gi∧Si
    5. None of the above
11. Which of the following are logically equivalent to the negation of "Some hipsters are either not cool or not good at philosophy"?
    1. ∀h. ~Hh ∨ ~(~Ch ∨ ~Ph)
    2. ∀h. Hh ⊃ (Ch ∧ Ph)
    3. (∀h. Hh ⊃ Ch) ∧ (∀h. Hh ⊃ Ph)
    4. All of the above
    5. None of the above
12. The Church-Turing Thesis
    1. Caused Stephen Hawking to give up his search for a Theory of Everything
    2. Provides reasons to study non-monotonic logic
    3. Proves Russell's Paradox
    4. Demonstrates the equivalence in expressive power of the Lambda Calculus and the Turing Machine
    5. None of the above
13. Which of the following properly distinguishes between use and mention in order to describe how a score of zero in tennis is described?
    1. Love means nothing to tennis players.
    2. "Love" means nothing to tennis players.
    3. Love means "nothing" to tennis players.
    4. All of the above
    5. None of the above
14. Gödel's First Incompleteness Theorem states that any classical, bivalent, logistic system capable of formalizing arithmetic on natural numbers must be:
    1. Sound but not complete
    2. Inconsistent or incomplete
    3. Unable to prove all of its theorems
    4. Incapable of capturing intuitive truths about the natural numbers
    5. All of the above
15. Who drew this comic?

    

    1. Randall Munroe
    2. Zach Weiner
    3. Gary Larson
    4. Donald Knuth
    5. None of the above
16. Lera Boroditsky's research has provided strong evidence for:
    1. Chomsky's assertion that there exists a universal grammar
    2. Agency is treated the same in all languages
    3. Language indeed shapes thought
    4. Language never shapes thought
    5. None of the above
17. Epiphenomenonalism is
    1. An emergent property of dynamic systems
    2. A reductionistic viewpoint
    3. Unrelated to the mind-body problem
    4. Rejected by scientific behaviorists
    5. None of the above
18. Foundalis takes issue with Diamond, Pinker, and Dawkins by asserting:
    1. Cognition arose only once in evolutionary history
    2. Cognition is separate from biology
    3. Cognition can be understood reductionistically
    4. Cognition is an emergent property of the brain
    5. None of the above
19. Dennett says:
    1. Consciousness itself is an illusion — a bag of tricks
    2. The hard problem of consciousness does not exist, in other words solving the easy problems solves the hord one
    3. Mechanistic explanations of how the brain works does not imply that people are not responsible for their actions
    4. All of the above
    5. None of the above
20. Neil deGrasse Tyson claims who of the following to be the smartest person who ever lived:
    1. Anaxagoras
    2. Muḥammad ibn Mūsā al-Khwārizmī
    3. Albert Einstein
    4. James Clerk Maxwell
    5. None of the above