Thursday, 27 August 2015

Saul Kripke’s Self-referential Sentence

Let 'Jack' be a name of the sentience 'Jack is short', and we have a sentence that says of itself that it is short. I can see nothing wrong with ‘direct’ self-reference of this type. If ‘Jack’ isn't already a name in the language, why can't we introduce it as a name of any entity we please? In particular, why can't it be a name of the (uninterpreted) finite sequence of marks ‘Jack is short’? …Yet if we name it ‘Jack’, it at once becomes meaningful and true. (Note that I am speaking of self-referential sentences, not self-referential propositions.)” (Kripke, 1975)

According to Saul Kripke, a sentence can say something “meaningful and true” about itself. Its sentential truth-condition (if there is such a thing) is the sentence itself. That is, its meaning is itself. In that case the truth, meaning, reference, etc. of the self-referential sentence aren't different from itself (which is usually the case with non-self-referential sentences). Would that mean that the meaning of “Jack is short” is Jack's being short or the sentence “Jack is short” itself?

We can, therefore, create a T-sentence thus:

The sentence “Jack is short” is true if and only if Jack is short.

Or perhaps the meaning of the sentence “Jack is short” is partly determined by that sentence’s own property – viz., shortness. In that case, the sentence “Jack is short” is true because this sentence is indeed short.

What would an alternative T-sentence look like in that case? We can have a reference to the sentence itself:

The sentence “Jack is short” is true iff the sentence “Jack is short” is true.

Note that we can't have:

The sentence “Jack is short” is true iff Jack is short.

because the right-hand side of the schema S would then be taken as a proposition rather than a sentence. If it's self-referential, the it can’t have a proposition or truth-conditions on the right side of the T-sentence.

So we can't have this condensed version either:

The sentence “Jack is short” is true iff p.

Nevertheless, perhaps we can have a truly non-self-referential part of the sentence in question. The word or name ‘Jack’ refers to the entire sentence of which it's a part. I said earlier that the sentence has no referent, truth-conditions, etc. outside itself. Despite having said that, it does appear to have a reference (or name) outside itself. We can separate the name ‘John’ from the sentence it usually belongs to (as Kripke does). The name ‘John’ therefore refers to the sentence in which it's also contained. Though can the sentence (or the name ‘John’ within the sentence) refer to anything outside of itself?

The sentence “Jack is short” must refer to itself. What about the name ‘Jack’ within the sentence? We've seen that the name ‘Jack’ can occur outside the sentence itself as a name for that sentence. Can the name in the sentence refer to anything outside the sentence? It's possible that the name inside the sentence could refer to the name outside the sentence. Though usually names can't name (or refer to) other names; especially to identical names which are, admittedly, in a slightly different context. Nevertheless, it's indeed the case that the name ‘Jack’ on the outside of the sentence is evidently different from the ‘Jack’ inside the sentence. The name on the outside of the sentence refers to the sentence of which it's a part; whereas the ‘Jack’ inside the sentence refers exclusively to itself qua sentence. So the outside ‘Jack’ refers qua name of a sentence. The inside ‘Jack’ refers qua sentence (or sentence meaning) rather than name itself. The name on the outside, ‘Jack’, simply names; though it doesn't describe (or refer) to the sentence’s meaning. On the other hand, with the inside ‘Jack’ the meaning of the sentence needs to be taken on board. That is, the inside ‘Jack’ would be taken as a meaningless part of a meaningless sentence if that sentence weren't taken to be about itself and also have the name ‘Jack’.

Again, if ‘Jack’ is on the outside of the sentence, then it's simply used to name - rather than describe - the sentence itself. If ‘Jack’ on the outside is taken exclusively as a proper name of the sentence, then it tells us nothing about the sentence: it simply refers to it or picks it out. At least this is part of a well-accepted position on proper names (by Kripke himself, amongst others). Though the name on the inside needs to be interpreted in order to function and give meaning to the sentence it is itself a part of.

Can we have a T-sentence if both sides of the schema are identical? Traditionally a T-sentence has a sentence on the left side and a proposition (or set of truth-conditions) on the right side. It could now be said that the self-referential T-sentence serves no purpose. Or we can say that it's not a genuine T-sentence at all. What it is is an identity statement (or tautology) such as:

The sentence “Jack is short” = the sentence “Jack is short”

Let’s turn to the name ‘Jack’ that refers to the sentence “Jack is short”.

This sentence, in turn, refers to itself. So the name ‘Jack’ on the inside therefore refers to itself. Does it refer to itself qua name or qua sentence? The inside ‘Jack’ clearly refers to the sentence "Jack is short". Yet the sentence is called ‘Jack’. Therefore the name ‘Jack’ on the outside names the sentence; though it isn't required to describe the sentence or offer us a meaning of it. “Jack is short” is itself called ‘Jack’. This means that the name ‘Jack’ on the inside also refers to the referent, as it were, of the name ‘Jack’ (to itself). So it follows that ‘Jack’ in the sentence uses the name ‘Jack’ (though does not refer to it) and refers to the sentence named ‘Jack’.

If the sentence is named ‘Jack’, then we can say that ‘Jack’ names ‘Jack’ (the sentence) and ‘Jack’ (the name). Therefore the name ‘Jack’, in the sentence, names both ‘Jack’ the name and ‘Jack’ the sentence. We can't even say that the name ‘Jack’ names Jack (without quotation marks). ‘Jack’ is never without quotation marks. We could say that ‘Jack’ names the sentence Jack (without quotation marks). Though if the sentence itself is named ‘Jack’, then when we name this sentence or refer to it we need to put that name or sentence in quotation marks. And if ‘Jack’ also names the ‘Jack’ within the sentence itself, it's still referring to a name that's also a name of the sentence itself. So in all cases the name ‘Jack’ refers to ‘Jack’ the name (of a sentence) and ‘Jack’ the name within the sentence. In that case, the name ‘Jack’, in this context at least, can never refer to the word Jack without quotation marks.

We appear to be left with a name of a name.

Can we have a name of a name that's not a name of anything else (other than itself)? Why name a name if that name is already a name? Of course we can refer to a name, as in:
“I'm referring to the name ‘Tony Blair’ that in turn refers to the man Tony Blair.”
I can also refer to a name in this way:
         “The name ‘Tony Blair’ has nine letters.”
These are references to names that actually refer. That is, the name 'Tony Blair' refers to the person Tony Blair. And even the second example refers to an inscription with nine letters. In the second case, therefore, we're referring to a name as also something with nine letters. We can therefore say that the name 'Tony Blair' also names something with nine letters as well as Tony Blair the man. In that case we could take the name 'Tony Blair' as not really being a name of something objectual that isn't a name because it's taken simply as referring to an inscription with nine letters. However, we could say that it is indeed referring to something that's not a name if it's referring, instead, to an entity with nine letters. Something that's taken exclusively qua inscription can't be a name as names are commonly understood. If 'Tony Blair' is taken only qua inscription and not qua name (of something), then we can say that the inscription 'Tony Blair' in the sentence “ ‘Tony Blair’ has nine letters” refers to an inscription not a name. So why can’t we say that the inscription 'Tony Blair' names, rather than simply refers to, an inscription with nine letters? The name 'Tony Blair' could therefore name something with nine letters. It can now be taken qua something with nine letters or qua name of a person. If 'Tony Blair' is taken qua name exclusively, it is therefore a name of itself. It's the name of its own inscription. And if taken qua something that names an inscription with nine letters, it's a name and also a referent (i.e., something with nine letters). Then the name 'Tony Blair' and the something with nine letters would be one and the same thing under two descriptions or “modes of presentation”:

(x) (PxQx)

The inscription 'Tony Blair' is intensional in this context. That is, 'Tony Blair' can be taken qua name (of itself) or qua something with nine letters. Extensionally, the name 'Tony Blair' and something with nine letters have the same extension – viz., the inscription 'Tony Blair'. Though, again, the inscription has two modes of presentation. The first mode is a mode that sees 'Tony Blair' as a name (of itself). And the other mode is a mode that sees 'Tony Blair' as an inscription with nine letters.

Can names name themselves?

Yes, if each particular inscription or utterance of the name is seen as a token of a type. That is, in the sentence

The name 'Tony Blair' names the name 'Tony Blair'.”

each example of the inscription 'Tony Blair' is seen as a token of the type 'Tony Blair'. We can't say “the type Tony Blair [without quotes]” because 'Tony Blair', in this context, is always an inscription or a name of itself. Therefore any use of it will require quotation marks.

We can now say that token name, 'Tony Blair', names the type name, 'Tony Blair'. However, unlike other examples of types and tokens, this example of a type and a token are identical. However, the two inscriptions of 'Tony Blair' in the above sentence aren't numerically identical because they have spatial and temporal differences. In this sense they can still be seen as tokens of a type.

We can now ask: Where is the type? Perhaps the type 'Tony Blair' is an abstract object. If that's the case, then we can in fact drop the quotation marks and use italics to symbolise the abstract object instead (i.e., Tony Blair). This italicised inscription can now be distinguished from 'Tony Blair' the name, 'Tony Blair' the inscription, and, indeed, Tony Blair the (concrete) person. Of course we may not really believe in the existence of abstract objects. Certainly not in the abstract object Tony Blair.

To recapitulate. We can say that the sentence “Jack is short” is short. Then we can have the sentence:

The sentence “‘Jack is short’ is short” is not as short as the sentence "Jack is short" on its own.

Firstly we had the sentence:

Jack is short.”

Then we had the sentence:

Jack is short” is short.

Now we can have:

The sentence “‘Jack is short’ is short” is (also) short.

And finally the sentence:

The sentence “The sentence ‘Jack is short’ is short” is not short.

Kripke says that the sentence “Jack is short” is an “(uninterpreted) finite sequence of marks”. One can wonder whether or not he can say such a thing if he also says the following about the self-referential sentence:

i) That ‘Jack’ is the name of the sentence “Jack is short”.

ii) That the sentence “Jack is short” refers to itself qua sentence.

iii) That the word ‘short’ means short as it applies to the sentence “Jack is short”.

iv) That the sentence takes on a subject-predicate form in which the name ‘Jack’ ( not the sentence Jack) is the subject and ‘is short’ is the predicate. If it were “uninterpreted”, it could have read: “Short is Jack.” (Kripke says that the name ‘Jack’ can be a name even if used only about that sentence.)

v) If the sentence were truly “uninterpreted”, it couldn't even have the status of being self-referential. If something is self-referential (or simply referential), then it must be interpreted.

Perhaps it's wrong to read the sentence “Jack is short” as interpreted before it's known that ‘Jack’ is a name for that sentence. That is, Kripke says that only after “we name [the sentence] ‘Jack’ ” does the sentence become “meaningful and true”. However, if “Jack is short” was indeed at first uninterpreted, then it wasn’t really a sentence at all – and not just an “uninterpreted” sentence either. If that's the case, Kripke could have used the pseudo-words

Slinmp zt bolk.”

as an example of a string of “meaningless marks”. Then we could indeed interpret it, such that the inscription “Slinmp” refers to the string of marks it is itself a part of. “zt” could mean is and “bolk” could mean short. Before this strained interpretation, we had indeed an “uninterpreted finite sequence of marks”. Now we have a sentence only because we have stipulated the (pseudo) meanings of the parts and the whole of that otherwise arbitrary inscription. However, without interpretation “Slinmp zt bolk” could still be self-referential. That is, we can say that the inscription

The sentence “Slinmp zt bolk” refers to the inscription “Slinmp zt bolk”.

Or even

Slinmp zt bolk.” = “Slinmp zt bolk.”

In addition, if the inscription is a token of a type, then this inscription may be identical to other inscriptions; though not numerically identical.


Kripke, Saul. (1975) 'Outline of a Theory of Truth'

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