Some Additional Thoughts on
‘Truth and Meaning’
Consider ‘Caesar was murdered, but it was not necessary that
Caesar was murdered’. Not only is this statement readily
intelligible, it is true. (IR p. 24)
It does not follow from this difference, however, that there is any
equivocation—any shift in meaning—between the two
occurrences of ‘was murdered’. Nor does it follow that it is illicit
to symbolize our statement in the form
‘P ∧ ¬ P’.
There is, then, no reason to doubt the legitimacy of the repeated
variables in Ramsey’s formula
‘B is a belief that P ∧ P’.
A confirmed extensionalist will not be moved by the parallel,
rejecting the logical form assigned the modal formula too.
Caesar was murdered  ¬( is analytic)
Caesar was murdered
They are not objects because ‘the way things are
thought to be when someone thinks that Running
Rein was four years old’ is not a genuine singular
term or Eigenname. (p. 27)
Well, it is grammatically. What makes it nongenuine?
1
(1)
2
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
2
1
1,2
6
(1,2),6
2,6
2,6
((1,2),6)(2,6)
(1,2),(1,2,2,6)
12
12
12
1
1,12
12
(1,12),12
12,((1,12),12)
(1,2),(1,2,2,6)
12,(1,12)
∀Q(δQ 
(Q  ¬P(δP ∧ P))
RδR
δR
δR  (R  ¬P(δP∧P))
R  ¬P(δP∧P)
R
¬P(δP ∧ P)
δR ∧ R
P(δP ∧ P)
¬R
¬¬P(δP ∧ P)
∃P(δP ∧ P)
δS ∧ S
δS
δS  (S  ¬P(δP ∧ P))
S  ¬P(δP ∧ P)
S
¬P(δP ∧ P)
¬P(δP ∧ P)
¬RδR
Premiss
Assumption, for reductio
2 Instantiation
1 I
3, 4 modus ponens
Assumption
5, 6 ∧E and modus ponens
3, 6 ∧I
8 I
7, 9 reductio, discharging assumption 6
5, 10 ∧-E and modus tollens
Assumption
12 Instantiation
13 ∧E
1 I
14, 15 modus ponens
13 ∧E
16, 17 ∧Eand modus ponens
12, 18 reductio, discharging assumption 12
11, 19 reductio, discharging assumption 2
We would also get into trouble if we applied our rules to
‘Everything a Cretan says should be rejected as untrue’. I
think we just have to concede that problems would arise if the
entire semantic machinery of the present paper were to be
projected into the object language: the limitations on such
projection mean (as in Kripke’s theory) that ‘the ghost of the
Tarski hierarchy is still with us’ (Kripke 1975, p. 714). But
the ghost is far less inhibiting than the hierarchy proper: the
rules proposed enable us to do a great deal of semantic
theorizing within our system.
If the (very substantial) ghost is not to be exorcised, why not
just stick with Tarskian hierarchialism? It’s pretty
straightforward and one can do a lot of semantic theorising
about the object language.
Not about the language of the semantic theory itself it’s
true[sic]- but the same is true on the above account.