Correct formulation of the Rule U.I. (Universal Instantiation) is ........... .
(X) (φx)
∴ φu
(where u is any individual symbol)
In Copi’s quantification theory, Universal Instantiation (U.I.) lets us infer any substitution instance of a propositional function from its universal quantification: (x)(φx) ∴ φν, where ν (nu) is any individual symbol.
Copi uses ‘individual symbol’ deliberately so that ν may be either an individual constant (a, b, c …) or an individual variable (x, y, z …). This is needed because in proofs U.I. is often applied to a variable, such as y, so that Universal Generalization can be used later.
Restricting ν to individual constants, as one formulation does, excludes instantiation to a variable. Restricting it to variables excludes constants. A version with no stated condition on the instantial symbol leaves the rule incomplete.
Hence, the answer is (X) (φx) ∴ φu (where u is any individual symbol).
Similar Questions
Match List I and List II and select the correct answer from the codes given below :
List I List II (a) ~ (p ∨ ~ p) (1) Identity (b) ~ (p • ~ p) (2) Contingency (c) ~ (p ⊃ q) (3) Tautology (d) p ⊃ p (4) Contradiction Codes :
(a) (b) (c) (d)
Which of the following is not the characteristics of an effective decision procedure ?
Law of contradiction states that :
Characteristics of an Axiomatic systems are ................. .
(1) Consistency
(2) Completeness
(3) Independence
(4) Contingent
Correct symbolization of the following proposition is — “All successful politicians and orators are hard-working”.
“Sudhir had not locked the gates yesterday. Either the watchman or Sudhir locks the gates. Therefore, the watchman must have locked the gates yesterday”. This argument is ..................... .
If the statement ‘p’ is true and the statement ‘q’ is false, the truth value of the statements ‘p ≡ ~ q’ and ‘~ q ⊃ ~ p’ are :
In the ranking of a competitive examination Vishal was above Vijay but below Shyam. Mohan was above Shyam but below Rohan. Vijay was between Vishal and Ashok. Who is third from the top ?
Ragini facing East walks 10 meter, then she turns to her left and walks 12 meter. Then she turns to her right in $45^o$ and walks 15 meter. Then, how much distance she has walked from the starting point and which direction is she facing now ?
In the Wason selection task for propositional reasoning, ‘participants develop a general idea of the rule, then construct examples that follow the rule’ is referred to as :
Important Questions from Deductive - Teaching
Match List I and List II and select the correct answer from the codes given below :
List I List II (a) ~ (p ∨ ~ p) (1) Identity (b) ~ (p • ~ p) (2) Contingency (c) ~ (p ⊃ q) (3) Tautology (d) p ⊃ p (4) Contradiction Codes :
(a) (b) (c) (d)
Which of the following is not the characteristics of an effective decision procedure ?
Law of contradiction states that :
Characteristics of an Axiomatic systems are ................. .
(1) Consistency
(2) Completeness
(3) Independence
(4) Contingent
Correct symbolization of the following proposition is — “All successful politicians and orators are hard-working”.
