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On Friday, February 17, 2017, Redacted sender jlsperanza for DMARC <
dmarc-noreply@xxxxxxxxxxxxx> wrote:
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 the case."
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.
Again,
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 shopping":
"The TLP begins "The world iis all that is the case" -
which seems simple and straighforward at one level, b
ut 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 careful).
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 like.
McEvoy quotes Witters as arguing that '[philosophical explanation has] to
stop somewhere.'
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 stops because
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.
Cheers,
Speranza
