# On The Limits of What Can Be Said

• From: wittrsl@xxxxxxxxxxxxx
• To: wittrsl@xxxxxxxxxxxxx
• Date: Wed, 21 Jul 2010 08:58:43 -0700 (PDT)

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I was a little reluctant to shoot ahead to these issues, but what the hell.
There's a very good discussion of what W had in mind with respect to the limits
of what can be said and what his reasons were in James Griffin's excellent book
"Wittgenstein' s Logical Atomism."  Here are some excerpts:

The Theory of types...seemed to lead to two incompatible states of affairs.
First, it required that the hierarchical order of types be strictly observed; a
type of order n, according to the theory, should have as arguments only types
of

order n-1 and should be an argument for only types of order n+1.  Now several
functions are, on this standard ambiguous as to type: functions, namely, which
can take arguments of several or all different orders.  Such functions, because
they do not hehave as the Theory of Types requires, are improper; they can lead
to contradiction and paradox; and what one tries to say with them, if there is
any sense to it at all, must be expressed in a different way....Then, secondly,
the Theory of Types made words like 'thing', 'property', 'relation', 'fact',
'type'', &c., important in logical vocabulary.  So the incompatibility is
between on the one hand, the theory's restriction on the behaviour of functions
and, on the other, the vocabulary which the theory itself makes important.  The
items in the vocabulary do not themselves meet the requirement.  'Type', for
example, can take an argumt of any order; 'function' can take an argument of
any

order except the first; &c.  Each is typically ambiguous.  However, W did not
think that this incompatibility called for revision in the Theory of Types.  He
thought, as we see in the Notes Dictated to Moore, that, much to the contrary,
it shows a theory of types to be altogether impossible.  To SAY something like
'M is a thing' uses the typically ambiguous word 'thing'.  To SAY that there
are

types or that a function can have as an argument only a type of an immediately
lower order makes use of the typically ambiguous words 'type', 'function', and
'argument'.  And these statements are what would make up a theory of types.
But

this does not leave logic in a difficult position, W says, because even were a
theory of types possible, it is unnecessary:

"Even if there WERE propositions of the form 'M is is a thing', they would be
superfluous (tautologous) because what this tries to say is something which is
already SEEN when you see 'M'." [Notes Dictated to Moore, 108.29-31]

So, a theory of types is both impossible and superfluous.  First, what it tries
to say cannot be said; second, what it tries to say is already SHOWN by the
symbolism.  In order to say about a certain sysmbol what the Theory of Types
wants to say, one would first have to know what the symbol is, and in knowing
this one would SEE the type....

"That M is a THING can't be SAID; it is nonsense: but SOMETHING is SHOWN by the
symbol 'M'."

"...that a proposition is a subject-predicate proposition can't be said: but it
is SHOWN by the symbol."

"Every REAL proposition SHOWS something, besides what it says, about the
Universe: or, if it has no sense, it can't be used; and if it has a sense, it
mirrors some logical property of the Universe." [NM  107-109]

...Just as only certain types of elements in the world can fit together to make
a fact, so only certain types of symbols can combine to make propositions.  In
this sense, propositions SHOW (mirror) the logical properties of the world....W
says that a language which did not mirror these properties, i.e an illogical
language, would be one in which "you could put an EVENT into a hole."

[All from Griffin, at 18-20]

One other related point made nicely by Griffin brings us back to the point we
discussed earlier about whether, according to W in TLP propositions are
themselves facts:

A substantive' s role in a sentence is to represent; a substantive is, as it
were, the deputy in a proposition for an object in the world.  A function is
quite different.  For example, the 'R' in 'aRb' differs from 'a' and 'b' in
that

it is not what symbolizes; what symbolizes is that it comes between the 'a' and
the 'b'.  That is, what symbolizes in 'aRb' are (i) the sign 'a', (ii) the sign
'b', and (iii) the FACT that 'R' comes between 'a and 'b'.  Propositions must
themselves be facts, the facts that their constituents have a particular
arrangement.  Thus, the function-part of a prop is a fact, while a name is not.

Also it is by makign a certain thing the case in a proposition sign that I say
that a certain thing is the case in the world.  Thus while names stand for
objects, arrangements of names say something about them; names represent,
functions assert.  [Griffin, at 16]

Some time prior to TLP, W put this as follows:

"Propositions, which are symbols having reference to facts, are themselves
facts

(that the inkpis on this table may express tha I sit in this chair)."  [Notes
on

Logic II, 11-13]

Anyhow, W's take on the realism-idealism controversy will turn out to be, I
think, that general statements about EVERYTHING simply can't make sense.  One
can show maybe, but not say.

Walto

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