Errata for The Principles of Mathematics Revisited by Jaakko Hintikka

Errata

? p. ix, l. -15

`This received': change `This' to `The'

p. 7, l. 3

`it is very nearly looks': delete `is' ?

p. 11, l. 11

`descriptive function of logical is': change `logical' to `logic'

p. 17, l. 7

`There is therrefore': change `therrefore' to `therefore'

p. 21, l. 14

`might all it': change `all' to `call'

p. 25, l. 13

`(G.E)': change to `(R.E)'

p. 25, l. 16

`(G.A)': change to `(R.A)'

p. 28, l. -4

`Diophantine games of number of': delete second `of'

p. 34, l. 11

`tobleau': change to `tableau'

p. 40, l. 23

`1923': change to `1922' ? (cf. References)

p. 43, l. 22

`though are': insert `there' after `though'

p. 46, l. 9

`fellow': insert `a' before `fellow'

p. 48, l. -14

`gametheoretical': change to `game-theoretical'

p. 50, l. -15

`that in cuts off': change `in' to `it'

? p. 52, l. 16...19

`Let S₀ be a formula of ordinary first-order logic in negation normal form. A formula of IF first-order logic is obtained by any finite number of the following steps': After a single step, S₀ is no longer a formula of ordinary first-order logic in negation normal form.

? p. 53, l. 18...22

Notation (x // Op): what if operator Op occurs more than once within the scope of the universal quantor? For example: (x // )(S₁[x] S₂[x] S₃[x]) ?

p. 54, l. 6

`an impotant unclarity': change `impotant' to `important'

p. 57, l. 18

`indpendent': change to `independent'

? p. 58, formula (3.24)

If x=z, then y=u and thus H(x, y) ~H(x, y), which is a contradiction!? Hence, (3.24) is simply false. This cannot be intended.

p. 60, l. -4

`In results like (d)': change `(d)' to `(D)'

p. 63, l. -13

`(vi) At this point': change `(vi)' to `(vii)'

p. 64, formula (3.48)

Add closing parenthesis at end.

? p. 64, formulae (3.49)

Function g corresponds to h in (3.47). Its function value does not depend on its second argument, which makes it unsuitable as a counterexample.

? p. 74, formula (4.3)

Add conjunct `(\epsilon0)' left of implication sign

p. 81, formula (4.17)

`S<sub>1</sub>': change to `S₂'

p. 111, l. 19

`etween': change to `between'

? p. 113, l. -1

`This relation will be called R(x, y)': Which relation gets named here? Furthermore, the name R is not used later on.

p. 117, l. -11

`x=S<sub>2</sub>': change `S₂' to `S₁'. Cf. clause (f) on p. 115.

? p. 119, l. 19

`to choose in quantifier moves': `in' ? (delete?)

p. 135, formulae (7.3) to (7.5)

Add, e.g. after formula (7.5), `where H(x, y) means `x has hobby y'.'

* p. 135, l. -13...-12

`, that is, that no two gentlemen have all their hobbies in common': This interpretation is incorrect; e.g. predicate (7.3) holds in the model with two gentlemen, both with the same two hobbies. Delete `, that is, that ... common'.

p. 137, l. 1

`(7.2)': change to `(7.4)'

? p. 148, l. -13...-11

`In other words, the symbol combination (x)¬ ... the symbol combination (x)¬': Change `(x)¬' to `¬(x)', and change `(x)¬' to `¬(x)' ?

p. 149, l. 1

`semantical rules': change `rules' to `rule'

p. 149, l. 5

`insider': change to `inside'

p. 150, l. 3

`two sentences that the true': change `the' to `are'

p. 150, l. -2

`apply it to an open formula. ¬T[x]': delete `.'

p. 171, l. 7

`because on apparently could': change `on' to `one'

p. 174, l. 3

`where n is the numeral representing n': change first `n' to `n'

p. 174, l. -17...-16

`the truth-condition of only first-order sentence asserts': change `sentence' to `sentences'

p. 178, l. 15...16

`If brief': change `If' to `In'

p. 180, l. 9

`What will happen? if we now use instead of ': delete `?', and change second `' to `'

p. 180, l. -18

`~p(n)': change `p' to `P'

? p. 180, l. -18

`is no abject that': `abject' ?

p. 186, l. 17

`If brief': change `If' to `In'

p. 186, formula (9.2)

`(z)': change to `(z)',

p. 186, formula (9.3)

Add interpretation that f and g are each other's inverse.

? p. 187, formulae (9.4) and (9.5)

Formula (9.4) does not match formula (3.48); `zy' should be `zu'? Formula (9.5) misses a conjunct corresponding to `zy' in (9.4). I do not believe these formulae capture the intended interpretation.

? p. 188, formula (9.6)

I do not believe it captures the intended interpretation.

p. 201, l. 11

`of historical example': insert `a' after `of'

p. 205, l. 17

`In so far as such as': change rightmost `as' to `an'

p. 206, l. 8

`the status of higher-order entities that have to do arise': delete `that have to do'; possibly insert `,' (comma) after `arise'

p. 206, l. 16

`for-reaching': change to `far-reaching'

p. 210, l. -6

`By the theory of type 1 mean': change `1' to `I'; possibly insert `,' (comma) after `type'

p. 221, l. 17

`is pre': change `pre' to `pre-'

p. 225, l. -18

`Thus on the constructivistic interpretation': change `on' to `in'

p. 228, l. 20

`to draw at least-': change `least-' to `least'

p. 231, l. -16

`to ordinary truth-functional conditional': insert `an' after `to'

p. 231, l. -14

`the analysis (10.13)': insert `of' after `analysis'