McEvoy was asking for an expansion re: the different implicatures, as it were,
regarding the denying of Witters's first utterance in TLP:
i. The world is all that is the case.
I must confess that, as I was reading McEvoy's original post ("Wittgenstein
sends us shopping"), I was, as is my wont, commenting sentence by sentence. So
when I got to the point when McEvoy explicitly talks about 'denying' (which I
provide below for easy reference), I came out with my 'not' utterance:
ii. It is not the case that the world is all that is the case.
-- only to see, one sentence by McEvoy later, that he had preferred the variant:
iii. It is false that the world is all that is the case.
In my commentary to that, I made a hasty point about Strawson's "truth-value
gap" theory (the phrase is originally Quine's), because it is H. P. Grice (who
calls a truth-value an unnecessary 'metaphysical concoction'), in commenting on
Strawson, draws a distinction between Strawson's
iv. The king of France is bald.
and its 'rejection' variants.
Grice lists four:
v. The king of France is not bald.
vi. It is not the case that the king of France is bald
(Grice is having in mind Strawson's section on "Not and ~" in Strawson's
"Introduction to Logical Theory" -- where Strawson notes that the strict
equivalent of "~" is "It is not the case that..." rather than "not"
simpliciter). And Grice adds:
vii. It is false that the king of France is bald.
And for good measure:
viii. It is not true that the king of France is bald.
So one has to be careful.
In the case of Witters, I would take this opportunity to see if it helps us
explore on Witters's point about [philosophical] explanations having to stop
_somewhere_ (this is not tautological -- surely "Why?" questions can be
iterated ad infinitum -- the potetial infinite if not the actual one).
"The king of France is bald" resembles "The world is all that is the case" in
that it is of the "S is P" form, rather than merely propositional like "It's
raining" (symbolised by p -- as Strawson asks in "Introduction to Logical
Theory": "what is "it"?"). So we may need first-order predicate calculus. Note
that Witters uses 'world' as qualified by the definite article (or iota
operator, if you must), "the": that, then, "the world," is the subject. What
follows is prefaced by 'is'. Cfr. Grice, "Aristotle on the multiplicity of
being". Is Witters, like, _defining_ 'the world' analytically?
ix. The world =df all that is the case.
I.e. is Witters's 'is' the is of 'identity' (as in (ix)) or the 'is' of
predication, as we need it in first-order PREDICATE logic? Since 'is' has only
one sense ("to not multiply senses of "is" beyond necessity"), one should not
trouble much by this. Taking the '=' is, granted, more complicated, in that we
have to define '=' by means of the Leibniz's law, or something like that. In
any case, suppose it is a predicate which is, if I may repeat myself,
predicated of "the world", i.e., that it has the property of "being all that is
In contexts like that, there may be an alleged ambiguity (but resolved by
disimplicature), if we assume, as Grice and I do, a bivalent interpretation of
'not,' or if we don't. In the second case, on top, we may adopt a mere
truth-value gap version (which I alluded to), as Strawson does (what if the
world is empty, say, or 'vacuous'?). But we may also get into further problems
if we adopt a many-valued (trivalent, etc.) interpretation of "not".
So back to McEvoy's remark:
"One might think that for many purposes "It is not the case that [the world is
all that is the case]" is interchangeable with "It is false that [the world is
all that is the case]."
McEvoy gives another example
"e.g. "It is not the case that Donal has two heads" and "It is false that Donal
has two heads". So where does the gap come in?"
Between both heads? Just teasing.
i. The world is all that is the case.
may be rendered as having the form:
x. The S is P.
And we are considering here something like
xi. 0(The S is P)
-- where "0" stands for "it is false that..." (Logicians use '1' for truth and
'0' for falsity -- versus variants with "~". (I actually prefer an inverted "T"
for 'falsity") -- and
xii. ~(The world is all that is the case).
So let's go back to the original fragment in McEvoy's "Wittgenstein sends us
"The TLP begins "The world iis all that is the case" - which seems simple and
straighforward at one level, but what would it mean to deny it? What picture is
given by saying "It is false
that the world is all that is the case". What else could be the case?"
McEvoy's phrasing, "what picture is given by..." may possibly be generalised to
ANY proposition of the form "It is false that..."
Note that in fact, when McEvoy asks, "What else could be the case?", he is not
proffering (if that's the expression) a 'rhetorical question':
In possible-world semantics, surely 'possible states of affairs' may be deemed
part of the world.
(I'm sure Popper, being a bit of a Meinongian, would consider a possible state
of affairs part of what Popper calls his 'third world'. So one has to be
Grice is not too explicit as to the differing implicatures for 'it is false
that...' and 'it is not the case that...'.
But I'm sure that in a Russellian expansion of his favourite "The king of
France is not bald", the different implicatures become clearer.
There are syntactical approaches to "not" (Hilbert's formalism) that need not
deal with the concept of 'falsity'. It is only a 'semantic' conception of 'not'
(alla Tarski) that ascribes a 'truth-table' to this unary operator. And the
differing implicatures between 'it is false that...' and 'it is the not the
case that...' are, of course, pragmatic, rather than semantic, in nature. So
one has to be careful, however 'interchangeable' these two idioms may seem
McEvoy quotes Witters as arguing that '[philosophical explanation has] to stop
This McEvoy retrieves from PI, rather than TLP, but as we see, even with the
very first proposal in TLP ("The world is all that is the case") we find that
counter-explanations to the effect that it may NOT be the case, to all
philosophers (Kripke, Leibniz), that the world is all that is the case.
These counter-explanations need, in turn, to be addressed by further
counter-counter-explanations (Imagine a succession of "Why"? questions). If the
series stops somewhere, Witters does not say where. Perhaps he implicates it.
Witters's point about the 'five' seems simpler. Witters is, like Ryle, a
behaviourist, and he thinks the explanation he gives making reference to the
way the shopkeeper ACTS (or 'behaves') is where the philosophical explanation
xiii. meaning =df use
for Witters, but never for Grice! In "Prolegomena" to "Logic and Conversation"
Grice actually makes a strong anti-Wittgensteinian point about this. If in
Wittgenstein's time, 'meaning is use' was considered sort of a truism, by the
time Grice is delivering his lectures, the opposite slogan ("meaning is not
use") seems to have become more fashionable. What Grice is having in mind may
well be Quine, who plays with 'meaning' and 'use' as applied to "if" in
"Methods of Logic" (and which Strawson discusses in his Introduction to
"Philosophical Logic" -- Oxford readings in philosophy).
And so on.