FYUG Even Semester Exam, 2024
Philosophy: Logic-II (Modern)

Subject: Philosophy
Course No.: PHISEC-151T
Semester: 2nd Semester (FYUG)
Exam Year: 2024
Time: 2 Hours
Full Marks: 50

Section-A

(Answer any fifteen questions. Each question carries 1 mark.)

1. "In a valid argument, if the premises are true conclusion must be true." Is the statement true?

True. In a valid argument, the truth of the premises necessitates the truth of the conclusion.

2. "Symbolic logic is also known as formal logic." Is the statement true?

True. Symbolic logic is often referred to as formal logic.

3. State any one characteristic of symbolic logic.

Symbolic logic uses artificial symbols or specialized notation to represent logical forms and relations.

4. "Verbal symbols are used in symbolic logic." Is it true?

False. Symbolic logic primarily uses non-verbal, artificial symbols rather than verbal symbols.

5. In indirect proof, what do we assume?

We assume the negation of the conclusion.

6. State the rule of Addition (Add).

The rule of Addition states: Given p, we can infer p v q.

7. State the rule of double negation (DN).

The rule of Double Negation states: p is logically equivalent to ~~p.

8. State the rule of transposition (Trans).

The rule of Transposition states: (p ⊃ q) is logically equivalent to (~q ⊃ ~p).

9. "One of the important decision procedure is the 'shorter truth table method'." Is it true?

True. The shorter truth table method is indeed a decision procedure.

10. "Indirect truth table method is also known as shorter truth table method." Is it true?

True. These terms are used interchangeably in modern logic.

11. What do we assume in indirect truth table method?

We assume that the argument is invalid by attempting to assign "True" to the premises and "False" to the conclusion simultaneously.

12. Give an example of an argument form.

Modus Ponens: p ⊃ q, p, therefore q.

13. 'Something is expensive' can be symbolized as:

(∃x)Ex.

14. Name a logician who is chiefly connected to quantification.

Gottlob Frege (or Bertrand Russell).

15. Name the rule which permits us to drop universal quantifier.

Universal Instantiation (UI).

16. "The difference between hypothesis and induction is one of degree." Is the statement true?

True.

17. How many kinds of hypothesis are there?

There are generally three kinds: Explanatory, Descriptive, and Working hypotheses.

18. Mention any one form of hypothesis.

Explanatory hypothesis.

19. Mention any one stage of hypothesis.

Verification.

Section-B

(Answer any five questions. Each question carries 2 marks.)

20. What is decision procedure?

A decision procedure is a mechanical method (like a truth table) that can determine in a finite number of steps whether an argument is valid or invalid, or whether a statement is a tautology.

21. What is variable?

A variable is a symbol (like x, y, z or p, q, r) that serves as a placeholder for any member of a specified set of values or propositions.

22. What is indirect proof?

An indirect proof is a method of proving validity by assuming the contradictory of the conclusion and showing that this assumption leads to a contradiction (reductio ad absurdum).

23. What is formal proof of validity?

A formal proof of validity is a sequence of statements where each statement is either a premise or follows from preceding statements by a valid rule of inference, ending with the conclusion.

24. What is the meaning of 'Reductio ad Absurdum'?

It means "reduction to absurdity"; a mode of argumentation that proves a statement by showing that its negation leads to a logical contradiction.

25. What is existential quantifier?

An existential quantifier is a symbol denoted as (∃x), meaning "there exists at least one x such that...".

26. What is working hypothesis?

A working hypothesis is a preliminary assumption used to guide an investigation, accepted provisionally without the expectation of it being the final truth.

Section-C

(Answer any five questions. Each question carries 5 marks.)

27. Construct formal proof of validity: [5 Marks]

1. H ⊃ (I v J)
2. ~I
/ ∴ H ⊃ J

Solution:

  1. H ⊃ (I v J) [Premise]
  2. ~I [Premise]
  3. H [Assumption for Conditional Proof]
  4. I v J [1, 3, M.P.]
  5. J [4, 2, D.S.]
  6. H ⊃ J [3-5, C.P.]

28. Use conditional proof to prove the validity: [5 Marks]

1. A ⊃ (B · C)
2. (B v C) ⊃ I
/ ∴ A ⊃ I

Solution:

  1. A [Assumption for C.P.]
  2. B · C [1, Premise 1, M.P.]
  3. B [2, Simp.]
  4. B v C [3, Add.]
  5. I [4, Premise 2, M.P.]
  6. A ⊃ I [1-5, C.P.]

29. Symbolise the following by quantifiers: [5 Marks]

  • (a) Some politicians are honest: (∃x)(Px · Hx)
  • (b) All flowers are beautiful: (x)(Fx ⊃ Bx)
  • (c) No dolphins are fish: (x)(Dx ⊃ ~Ix)
  • (d) All mathematicians are philosophers: (x)(Mx ⊃ Lx)
  • (e) All artists are not philosophers: (x)(Ax ⊃ ~Lx)

30. Test the following by shorter truth table method: [5 Marks]

Z ⊃ Y
X ⊃ W
Z v W
/ ∴ Y v X

Analysis: To prove invalidity, we seek an assignment where Premises are True and Conclusion is False.

XYZWZ ⊃ YX ⊃ WZ v WY v X
FFTTFTTF

Result: If we assign Z=T, Y=F, the first premise (Z ⊃ Y) becomes False. Through trial of all assignments where the conclusion is False (Y=F, X=F), we find that we cannot make all premises True while the conclusion is False. Thus, the argument is Valid.

31. Define probability. Distinguish between chance and probability. [2+3=5 Marks]

Probability: It is the mathematical likelihood of an event occurring, expressed as a ratio between the number of favorable cases and the total number of equally likely cases.

Distinction:

  • Chance: Refers to the unpredictability or the absence of a visible cause for an event; it is often used in a non-mathematical, everyday context.
  • Probability: Is a quantifiable measure based on logical evidence or statistical frequency; it provides a degree of certainty for a hypothesis.

Exam Focus Enhancements

  • Exam Tips: When using the shorter truth table method, always start by making the conclusion False and work backwards through the premises.
  • Common Mistakes: Do not confuse Universal Generalization (UG) with Universal Instantiation (UI). UI drops the quantifier, while UG adds it.
  • Legitimate Conditions of Hypothesis: A good hypothesis must be verifiable, consistent with established facts, and have predictive power.
  • Answer Presentation Strategy: For formal proofs, clearly label each step with the line numbers and the rule applied (e.g., 1, 3, M.P.).