Study Guide

Logic Midterm Study Guide: Spring 2019

I. Concepts

True or False? (15 – 20 questions @ 1 point each)

Logical Possibility, Necessity, and Contingency

  • How do we understand logical possibility in terms of ‘possible worlds’? What is the difference between logical possibility and physical possibility? Are some things that are physically impossible logically possible? What things are logically possible? What is not logically possible?
  • What is meant by ‘necessary’ and ‘contingent’ and how are they understood in terms of the notion of logical possibility and in terms of ‘possible worlds’?

Belief, justification and knowledge

  • How do we understand knowledge on the JTB account?
  • What is it for a belief to be justified? Can beliefs be true but unjustified? Can they be false but justified? Can rational, unprejudiced people who’ve got all available evidence and made every effort to learn the truth still disagree?

Rationality and decision-making

  • It is controversial whether it is ever rational to adopt a belief without compelling evidential reasons: what sorts of cases suggest that it is rational?
  • What is Pascal’s Wager, how does it work and what is it supposed to show? Is it an argument for the existence of God? If not, what is it? Is Pascal assuming that it is or that it is not rational to adopt a belief without compelling evidential reasons?

Arguments and conditionals

  • What roles do premises and conclusion play in an argument? What makes an argument deductive? What makes an argument inductive?
  • What is a conditional? What are the parts of a conditional? How is a conditional falsified? How are conditionals similar to and different from arguments? Can they figure as parts of arguments?
  • What are necessary and sufficient conditions? Can you answer questions that ask whether something is necessary or sufficient for something else? In a conditional, what is necessary for what and what is sufficient for what?


  • What is it for an argument to be deductive? How do deductive and inductive arguments differ? What is it for an argument to be valid? What is it for an argument to be sound?
  • How does “logical form” relate to validity given our assumption that validity is to be understood as formal validity? What is it for an argument to be a counterexample to another argument? How does the method of counterexample work to show invalidity? Can it show validity?

Truth functions

  • What is a function? Which relations are functions and which aren’t?
  • What is it to say that the connectives of propositional logic are ‘truth functional’?
  • What do we mean by saying some ordinary English connectives are not truth functional? What are some examples of ordinary English connectives that are not truth functional?

II. Tautologousness, Equivalence, Consistency, and Validity

      What, if anything, can you infer about the validity or invalidity of an argument given incomplete information: ‘V’ for ‘must be valid’; ‘I’ for ‘must be invalid’; or ‘?’ for not enough information—could go either way. (multiple choice: 5 questions @ 1 point each)

III. Identifying Conclusions

Which statement is best understood as the conclusion of each of the following arguments?
(multiple choice: 5 arguments @ 1 point each)

IV.  Propositional Logic Translation

Which of the following symbolized sentence(s), if any, correctly translate the following English sentences? For the purposes of this question, consider logically equivalent sentences equally good (of bad) translations. Remember De Morgan’s Laws equivalences! (multiple choice: 5 questions @ 1 point each)

V. Truth Table

Show your work! –that is, do the whole truth table putting ‘T’ or ‘F’ in every row of each column under a letter or connective as appropriate and put boxes around the column(s) under main connective(s) (1 question @ 5 points: 5 total)

VI. Truth Tree

Refer to the completed truth tree below to answer the multiple choice questions that follow: 5 questions @ 1 point each.