On The Limits of What Can Be Said

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

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 

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 

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 

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.  

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 

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 

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

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.



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