Philosophy 5318, Spring 2021
Logic
Alexander R. Pruss
E-mail:
alexander_pruss@baylor.edu
Course
web page: http://AlexanderPruss.com/classes/logic
Class times: Tu Th 11:00-12:15 in Morrison 108
Instructor office hours: MH 213 and by Zoom: Mon and Wed, 10:50 am - noon
Abstract:
The point of this course is to gain some formal tools that are useful in a wide-range of areas of philosophy:
á Propositional logic
á Quantificational logic
á Basic set theory
á Basic probability theory
á Basic modal logic
Grading and
requirements:
á Three tests worth 15% each: propositional/quantificational logic, set theory, and modal logic / probability.
á Weekly assignments worth 55%. Most of these will be exercises. A few might ask for brief philosophical reflection.
Academic integrity:
Credible suspicions of lack of academic integrity will be typically reported to the University for further investigation. My default penalty for a failure in academic integrity is an F in the class. Plagiarism, impermissible forms of cooperation, etc. all count as failures of academic integrity.
Sickness/COVID-19 policy
Please wear proper, effective face-covering and space yourself out from other people as much as you can.
I am committed to making the classes available for electronic attendance. Even if you only have very minor symptoms, please stay home, and be tested for COVID-19. And even if the test comes back negative, please donÕt spread influenza or even the common cold in this difficult time.
The course may need to be converted to an electronic-only class. If so, we will switch to synchronous online meetings.
Reading assignments:
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Tue Jan 19 |
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Thu Jan 21 |
LPL start-4.4 (lots of pages, but you should know almost everything in chapters 1-3 already) |
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Tue Jan 26 |
LPL 4.5-4-6, 5.1-8.2 (chapters 5 and 7 should be a quick skim) |
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Thu Jan 28 |
LPL 8.3 |
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Tue Feb 2 |
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Thu Feb 4 |
LPL 9.1-10.4, 11.1-11.2 (most of this should already be familiar) |
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Tue Feb 9 |
LPL 11.3-11.5 |
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Thu Feb 11 |
LPL 12.1-12.4, 13.1-13.4 (chapter 12 should already be familiar) |
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Tue Feb 16 |
LPL 14.1-14.3 |
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Thu Feb 18 |
LPL 15.1-15.3 |
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Tue Feb 23 |
Test 1 (up to 14.3) |
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Thu Feb 25 |
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Tue Mar 2 |
LPL 15.4-15.6 |
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Thu Mar 4 |
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Thu Mar 11 |
LPL 15.7-15.9 |
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Tue Mar 16 |
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Thu Mar 18 |
LPL 15.10 |
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Tue Mar 23 |
LPL 16.1-16.3 |
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Thu Mar 25 |
More on induction |
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Tue Mar 30 |
GodelÕs incompleteness theorem |
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Wed Mar 31 |
Take-home Test 2: Chapters 15 and 16 |
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Thu Apr 1 |
Probability theory |
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Tue Apr 6 |
Conditional probability |
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Thu Apr 8 |
Bayes' theorem |
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Tue Apr 13 |
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Thu Apr 15 |
Konyndyk 1.1-1.4, 2.1-2.3 |
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Tue Apr 20 |
Konyndyk 2.4 |
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Thu Apr 22 |
Konyndyk 2.5-2.6 |
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Tue Apr 27 |
Konyndyk 3.1-3.4; Konyndyk 4.1-4.14 |
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Final exam period |
Test 3 |
Homework:
Homework due on a day when we have class is due before the beginning of
class. Homework due on a day when we do not have class is due at 11:59 pm.
Note: If any homework is for a section that was not yet covered in
class, it should count as automatically moved to the next homework due date.
Submit electronically whatever can be submitted
electronically, and put everything else in the instructor's mailbox.
á Due January 26:
o LPL 1.2, 1.9, 1.14 (this may require doing 1.13 informally), 1.22, 2.1, 2.18, 2.27, 3.3, 3.21. Bonus: Find a sentence S using the atomic sentences A, B and C which has the following truth table:
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A |
B |
C |
S |
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F |
F |
F |
F |
|
F |
F |
T |
T |
|
F |
T |
F |
T |
|
F |
T |
T |
F |
|
T |
F |
F |
T |
|
T |
F |
T |
F |
|
T |
T |
F |
T |
|
T |
T |
T |
T |
á Due Feb 4:
o LPL 4.39, 5.22 Ñ remember that this is an informal proof, 6.5, 6.6, 6.8, 6.14, 6.19, 6.32, 6.40, 6.41, 7.7, 7.8, 7.12 (I recommend you do the 7.13 check), 7.18 (the computer might be wrong for one of these), 8.21, 8.24, 8.26, 8.32, 8.36.
á Due Feb 11:
o LPL 9.7, 9.9, 9.19, 11.4, 11.5, 11.11, 11.21 (I think #9 has multiple interpretations, and the computer might not like the best oneÑat least that was true wit the previous editionÑso just do your best)
á Due Feb 16:
o LPL 10.1, 10.24, 10.25, 13.6, 13.8, 13.16, 13.26, 13.30, 13.33. Bonus: 13.29. Talk to me if stuck on anything other than the bonus.
á Due Feb 23:
o LPL 13.50, 13.55, 13.56, 14.2, 14.3, 14.12, 14.21, 14.28. Bonus: Let L be a dialect of First Order Logic containing only one predicate, Horse(x), meaning that x is a horse. In particular, L does not contain =. Informally show that there are no sentences of L that say ÒThere is exactly one horse.Ó
á Due Mar 2:
o LPL 15.2, 15.6, 15.8, 15.12
á Due Mar 10 (!):
o LPL 15.21, 15.31, 15.40
á Due Mar 16:
o LPL 15.62, 15.64, 15.65
á Due Mar 23:
o LPL 15.71
á Due Mar 30:
o LPL 16.1, 16.2, 16.14, 16.19. Bonus: 16.11, 16.30, 16.32.
á Due Apr 6:
o 1. (a) Consider a circular spinner hanging on a wall, where the spinner has an equal chance of ending up pointing in any direction, with the vertically upward being 0 degrees, the 3 oÕclock position being 90 degrees, the 9 oÕclock position being 270 degrees, and so on. Remember that the spinner can land at real-number angles that arenÕt integral numbers of degrees, say at 10.847747 degrees. Suppose that the spinner is spun twice, independently. Give intuitive arguments for what the probabilities of the following events are (i) The first spin landed at exactly 47.2; (ii) The two spins landed within 10 degrees of one another; (iii) The first spin landed within 15 degrees of 270 and the second landed within 3 degrees of 123.
o 2. (b) Describe a single infinite sample space in which all the events (i)-(iii) can be defined.
o 3. Informally prove that if A and B are disjoint events, then P(A intersect B)=0. ("intersect" is the intersection symbol)
o Bonus: Kahneman and Tversky gave people the following story: ÒLinda is 31-years-old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.Ó They asked if it's more likely that (a) Linda is a bank teller, or (b) a bank teller and feminist? 85% of respondents said that (b) was more likely. Prove from the axioms of probability that the respondents were wrong on a literal reading of the question. Give a charitable explanation of the mistake.
á Due Apr 13:
o 1. (a) Suppose that you have three fair (i.e., all outcomes are equally likely) dice tossed independently and simultaneously. What is the relevant sample space for looking at outcomes?
o 2. (b) What is the probability that all the dice will show the same number, and why?
o 3. Choose two of the following fallacies of probabilistic reasoning, and give a plausible sounding philosophical argument (in any area of philosophy) that commits the fallacy. Then supply plausible numbers for all the relevant probabilities and conditional probabilities, and do a Bayesian calculation to see if the argument can be salvaged. In the following "p makes q likely" means P(q|p)>1/2, and something holds "probably" provided that it holds with probability greater than 1/2 given the evidence. If really stuck for a philosophical argument, give a plausible sounding argument in another discipline.
1. p is true; p incrementally confirms q; q entails r; therefore, p incrementally confirms r
2. p is true; p entails q; q makes r likely; therefore, probably r
3. p is true; p entails q; q incrementally confirms r; therefore, probably r
4. p is true; q is true; p makes r likely; q makes r likely; therefore, probably r
5. p or q is true; p makes r likely; q makes r likely; therefore, probably r
o 4. Consider the hypothesis H that all ravens are black. Suppose you randomly choose a raven (from the pool of all ravens, of which there are nÑsome finite number) and notice itÕs black. Intuitively, this is evidence for H. Use Bayes' theorem, along with reasonable assumptions about conditional probabilities, to show this.
o Bonus: Consider the hypothesis H* that all non-black things are non-ravens. By parallel with problem 3, taking a random non-black think and noticing that it's not a raven should be evidence for H*. For instance, looking at a non-black sock and noticing that it's a non-raven seems to be evidence for H*. But H* is logically equivalent to the hypothesis H in 3. So, it seems that looking at a non-black sock and noticing that it's not a raven is evidence for H. But that's absurd. Find a plausible way to resolve this paradox.
á Due Apr 22 (!):
o Konyndyk 1.5.2.d, 2.1.e.C, 2.1.h.A (yes or no for each suffices), 2.1.h.B, 2.3.1-3 (see correction), 2.3.g.A (in S4). Bonus: 2.4.b.5, 2.4.b.7 (in S4).
o Correction (if you have the same edition as I do): The left hand side in on p. 32 in Exercise 2.3.2 should be: ~M(Lp&~Mq). The book has Lq instead of Mq.
á Due Apr 29:
o Konyndyk 3.4.2 (assume p has no free variables), 4.8.3.
o Give a complete formal proof of the Barcan formula.
o Use possible worlds and a reflexive accessibility relation (i.e., T) to prove informally that if itÕs not the case that everything is essentially a non-unicorn, then possibly there is a unicorn.
o Use possible worlds and a reflexive, symmetric and transitive accessibility relation (i.e., S5) to prove that if necessarily everything that is F is G, then necessarily anything that is essentially F is essentially G.
o Bonus: Come up with, and explain, an alethic modal operator that satisfies T but not S4. Try to make it not be too gerrymandered.
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