Note 37

"Predicability" and "predicable" still in the special sense as we have used them throughout our Section on the paradoxes, for instance (as explaining this use, and distinguishing it from the ordinary use) :

The term  ' red '  is predicable (in the usual sense) of a term standing for a red thing ( ' the curtain is red ' ).
If this term  ' red '  were also predicable (in the usual sense) of the term  ' the term red '  ( ' the term red is red ),  then it would be "predicable" (and otherwise it would be "impredicable" ).

This property (of something to be) "predicable" can indeed be possessed by certain concepts or terms, for example it is possessed by the term  ' (a) being '.  We can say :

the term  ' a being '  is itself a being,

(in this case a being of reason).
While in the business of signifying this being here, or that being there, or that being overthere, the term  ' a being '  also refers to itself  (that is, the term  ' a being '  refers (also) to the term  ' a being ' ),  because -- according to the proposition -- it (i.e. the term  ' a being ' )  is itself also a being.
Here we have an instance  of  self-reference  of  a  term, but this (instance of) self-reference is not total or complete, because in addition to referring to itself, the term also refers (disjunctively) to other entities.

Not so with the term "impredicable".
Because "impredicable" is (like 'red' or 'a being' )  also a term, we might wonder whether it is (like the term  ' a being ' )  "predicable", that is, we might ask whether it possesses the property "predicable" (or not). If we assume it does, then we can express this as follows :

the term "impredicable" is itself "impredicable".

And we know that this involves a contradiction, because we assumed that the term "impredicable" was "predicable".

If, on the other hand, we assume the term "impredicable" not to possess the property "predicable", then we can express this as follows :

the term "impredicable" is itself "impredicable",

but then again (as we know) a contradiction arises, because the term is then, according to this statement, "predicable", while we had assumed it not to be so ( = not to have this property).

So why do we here end up in paradox (both alternatives lead to contradiction), while in the case of the term  ' a being ',  and similar terms, we do not get stuck in a paradox?
The answer, according to me, is that while the  self-reference  of the term  ' a being '  is, as we saw, not complete, it  is  complete in the case of the term "impredicable". Here the term "impredicable", figuring in the proposition  ' the term "impredicable" is itself "impredicable" ',  totally embodies a property, and it refers to this property, so the self-reference is total, or, in other words :  the term "impredicable" refers to a property, but in doing this it refers (according to the proposition) to itself, and this is total self-reference. Again, this same state of affairs expressed in yet another way :  "impredicable" is a property of certain terms (like, for instance the term  ' a being ' ).  The term "impredicable" intends this property, that is, refers to this property. But this term itself is also "impredicable" (according to the above proposition), in the same way as is the case with the term  ' a being '.  But while the term  ' a being ,'  refers, in addition to itself, also to other beings, the term "impredicable", while referring to itself, does not refer to other things or beings, but to a property of them. And this property is the property "impredicable". So our term "impredicable" only refers to "impredicable" and to nothing else. And again, this is total self-reference. And, as we will show later, total self-reference cannot exist. So if we have come up with something that happens to be totally self-referential, then we must abandon it, because it is nothing.

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