Reasoning

Logic and Fallacies

1,716 Questions

Understand the fundamentals of propositional logic, logical inference rules, and paradoxes. This set includes identifying logical fallacies, including those found in classical Nyaya logic. Strong grasp of these concepts is crucial for scoring well in the reasoning sections of competitive tests.

Propositional logic modelsLogical inference rulesTypes of logical fallaciesParadoxes and contingent truthsNyaya logic concepts

Logic and Fallacies Questions

Multiple choice

What is the semantics of modal logic?

  1. The semantics of modal logic is defined in terms of possible worlds and accessibility relations.

  2. The semantics of modal logic is defined in terms of truth values and logical connectives.

  3. The semantics of modal logic is defined in terms of sets of propositions and logical connectives.

  4. The semantics of modal logic is defined in terms of agents and actions.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The semantics of modal logic is defined in terms of possible worlds and accessibility relations. A possible world is a complete and consistent set of propositions, and an accessibility relation is a relation between possible worlds that determines which worlds are accessible from each other.

Multiple choice

What is the principle of universal instantiation in modal logic?

  1. If a proposition is true in all possible worlds, then it is true in the actual world.

  2. If a proposition is true in some possible world, then it is true in the actual world.

  3. If a proposition is true in all possible worlds that are accessible from the actual world, then it is true in the actual world.

  4. If a proposition is true in some possible world that is accessible from the actual world, then it is true in the actual world.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The principle of universal instantiation states that if a proposition is true in all possible worlds, then it is true in the actual world. This principle is used to derive new theorems from modal logic axioms.

Multiple choice

What is the Barcan formula in modal logic?

  1. For any proposition ϕ, ◇□ϕ → □◇ϕ.

  2. For any proposition ϕ, □◇ϕ → ◇□ϕ.

  3. For any proposition ϕ, ◇□ϕ → ϕ.

  4. For any proposition ϕ, □◇ϕ → ϕ.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The Barcan formula is a theorem of modal logic that states that if a proposition is necessarily possible, then it is possibly necessary. This formula is often used to argue for the existence of necessary beings.

Multiple choice

What is the converse Barcan formula in modal logic?

  1. For any proposition ϕ, ◇□ϕ → □◇ϕ.

  2. For any proposition ϕ, □◇ϕ → ◇□ϕ.

  3. For any proposition ϕ, ◇□ϕ → ϕ.

  4. For any proposition ϕ, □◇ϕ → ϕ.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The converse Barcan formula is a theorem of modal logic that states that if a proposition is possibly necessary, then it is necessarily possible. This formula is often used to argue against the existence of necessary beings.

Multiple choice

What is the Gödel-Löb theorem in modal logic?

  1. If a proposition ϕ is provable in a modal logic system, then □ϕ is also provable.

  2. If a proposition ϕ is provable in a modal logic system, then ◇ϕ is also provable.

  3. If a proposition ϕ is refutable in a modal logic system, then □ϕ is also refutable.

  4. If a proposition ϕ is refutable in a modal logic system, then ◇ϕ is also refutable.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Gödel-Löb theorem is a theorem of modal logic that states that if a proposition is provable in a modal logic system, then its necessity is also provable. This theorem is often used to argue for the existence of God.

Multiple choice

What is the completeness theorem for modal logic?

  1. Every consistent modal logic system has a model.

  2. Every consistent modal logic system has a finite model.

  3. Every consistent modal logic system has an infinite model.

  4. Every consistent modal logic system has a countable model.
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A Correct answer
Explanation

The completeness theorem for modal logic states that every consistent modal logic system has a model. This theorem is often used to prove the soundness and completeness of modal logic systems.

Multiple choice

What is the decidability problem for modal logic?

  1. Is there an algorithm that can determine whether a given modal logic formula is satisfiable?

  2. Is there an algorithm that can determine whether a given modal logic formula is valid?

  3. Is there an algorithm that can determine whether a given modal logic system is consistent?

  4. Is there an algorithm that can determine whether a given modal logic system is complete?
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A Correct answer
Explanation

The decidability problem for modal logic is the question of whether there is an algorithm that can determine whether a given modal logic formula is satisfiable. This problem is undecidable, meaning that there is no such algorithm.

Multiple choice

Which of the following is NOT a branch of mathematical philosophy?

  1. Logicism

  2. Intuitionism

  3. Formalism

  4. Algebraic Geometry
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Algebraic Geometry is a branch of mathematics, not mathematical philosophy.

Multiple choice

Which of the following is a key concept in formalist philosophy of mathematics?

  1. Axioms

  2. Deductive Reasoning

  3. Mathematical Objects

  4. Proofs
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A Correct answer
Explanation

Axioms are a fundamental concept in formalist philosophy of mathematics, as they serve as the starting point for deductive reasoning and the construction of mathematical theories.

Multiple choice

What is the name of the philosophical principle that states that a mathematical statement is true if and only if it can be proven using a finite number of steps?

  1. Law of Excluded Middle

  2. Principle of Mathematical Induction

  3. Completeness Theorem

  4. Hilbert's Program
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The Principle of Mathematical Induction is a fundamental principle in mathematics that allows one to prove statements about all natural numbers by showing that the statement holds for the first natural number and that it implies itself for the successor of any natural number.

Multiple choice

What is the name of the philosophical principle that states that a mathematical statement is true if and only if its negation leads to a contradiction?

  1. Law of Excluded Middle

  2. Principle of Mathematical Induction

  3. Completeness Theorem

  4. Proof by Contradiction
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Proof by Contradiction is a fundamental principle in mathematics that allows one to prove a statement by assuming its negation and showing that this leads to a contradiction, thus establishing the truth of the original statement.

Multiple choice

What is the name of the philosophical principle that states that a mathematical statement is true if and only if it can be verified through empirical observation?

  1. Law of Excluded Middle

  2. Principle of Mathematical Induction

  3. Completeness Theorem

  4. Empiricism
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D Correct answer
Explanation

Empiricism is a philosophical principle that states that a mathematical statement is true if and only if it can be verified through empirical observation, emphasizing the role of experience and sensory evidence in mathematical knowledge.

Multiple choice

What are the three horns of the Münchhausen Trilemma?

  1. Infinite regress, circular argument, and unjustified assumption.

  2. Deduction, induction, and abduction.

  3. A priori knowledge, a posteriori knowledge, and synthetic knowledge.

  4. Objective knowledge, subjective knowledge, and intersubjective knowledge.
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A Correct answer
Explanation

The three horns of the Münchhausen Trilemma are infinite regress, circular argument, and unjustified assumption. Infinite regress occurs when a belief is justified by another belief, which is in turn justified by another belief, and so on, without ever reaching a stopping point. A circular argument occurs when a belief is justified by itself. An unjustified assumption occurs when a belief is not justified by any other belief.

Multiple choice

What is an analogy?

  1. A comparison between two things that are similar in some respects.

  2. A logical fallacy that occurs when two things are compared that are not similar.

  3. A type of argument that uses evidence to support a conclusion.

  4. A method of reasoning that uses deductive logic to reach a conclusion.
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A Correct answer
Explanation

An analogy is a comparison between two things that are similar in some respects. Analogies are often used to explain or illustrate a point.

Multiple choice

Which of the following statements is an example of a contingent truth?

  1. All bachelors are unmarried.

  2. All dogs are mammals.

  3. The sun is a star.

  4. Paris is the capital of France.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A contingent truth is a statement that is true in some possible worlds but not in others. The statement "The sun is a star" is a contingent truth because it is possible to imagine a world where the sun is not a star.