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) (Px ≡ Qx)

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.

Reference

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

Wittgenstein's Generalisations About Generalisations

Firstly here's a quote from the philosopher Gilbert Ryle in which he talks about Wittgenstein’s general distaste for generalisations:

“…he now [i.e., the late Wittgenstein] avoids any general statement of the nature of philosophy, not because this would be to say the unsayable, but because it would be to say a scholastic and therefore an obscuring thing. In philosophy, generalizations are unclarifications. The nature of philosophy is to be taught by producing concrete specimens of it.” (1951)

So what about Wittgenstein himself? He wrote:

“Our craving for generality has [as one] source … our preoccupation with the method of science. I mean the method of reducing the explanation of natural phenomena to the smallest possible number of primitive natural laws; and, in mathematics, of unifying the treatment of different topics by using a generalization. Philosophers constantly see the method of science before their eyes, and are irresistibly tempted to ask and answer in the way science does. This tendency is the real source of metaphysics, and leads the philosopher into complete darkness. I want to say here that it can never be our job to reduce anything to anything, or to explain anything. Philosophy really is 'purely descriptive'.” (1933-1935)

When Wittgenstein used the phrase “craving for generality” to express his position towards what he saw to be Western philosophy’s prime vice, he was himself generalising about Western philosophy.

To state that

All traditional Western philosophy generalises about things which can't be captured by such generalisations.

is to generalise (even if we drop the quantifier “all”). Similarly, the statement that

All traditional philosophy is “concerned with the general rather than the particular”.

is itself concerned with the general (i.e., all Western philosophy) rather than the particular.

If one classes oneself as a Wittgensteinian particularist (even if one doesn't actually use that term), that statement is a generalisation about those who can be called generalists and also about what can be called generalism. (For that matter, it's also to implicitly generalise about particularists and particularism.) It's of no consequence at all if particular Wittgensteinians don't use these terms (or indeed any ists or isms). They may not use such words; though they're still tacitly committed to the concepts which these words express.

To repeat:

“All generalizations are unclarifications.”

is a generalisation about (all) generalisations.

In order for Wittgenstein’s position to have a point (or in order for him to demonstrate his own point) there must be (or there needs to be) at least one generalisation that's not an “unclarification”. Though if there's at least one such generalisation that isn't also an unclarification, perhaps it could be (as Wittgensteinian might have claimed) the very generalisation that

“All generalisations are unclarifications.”

If the initial generalisation isn't taken to be the sole exception to what it claims, then it can be rewritten in this way:

All generalisations - including this one - are unclarifications.

This self-referential statement therefore allows itself to be either an exception to itself (i.e., if it didn’t include the central clause) or to be an actual example of what it claims. Though if it's not an exception to its own claim, then it too must be an unclarification. If it is an exception to what it claims, then there it may be the one and only one exception. Thus

All generalisations - including the one you're now reading - are unclarifications.

can be taken as a kind of proof (or just an example) of what it claims (i.e., if it's actually taken as an unclarification). If the statement about all generalisations implies (or entails) that it too is a generalisation (if about generalisations), then it must also suffer from the same kind of unclarity that's taken to be a property of all other generalisations.

However, Wittgenstein's statement about all generalisations is a second-order (or metalinguistic) generalisation. That is, it's a generalisation about generalisations: not a generalisation about events or things which aren't themselves taken to be linguistic generalisations. If all first-order generalisations (i.e., those in the “object language”) are unclarifications, then a second-order generalisation about first-order generalisations can be seen either being free from the property unclarity (i.e., due to its second-order status); or as being itself a victim of such a property (i.e., perhaps it's not an actual or genuine metalinguistic statement).

Note: Lycan's Paradox (at least according to Michael Clark) also deals with generalisations. More specifically, it deals with the statement, “Most generalisations are false". It states that “a minority [of generalisations] must be true”. However, since Wittgenstein's own meta-generalisation is about generalisations (one which claims they're all false or unclarifications), it's even less likely to be true than the first-order generalisations it has as its target.

References

Ryle, Gilbert. (1951) 'Wittgenstein', from Analysis, vol. 12, pp. 1-9
Wittgenstein, Ludwig. (1946-1949) Philosophical Investigations
-- (1933-1935)The Blue Book

Heterological & Homological Metalinguistic Statements

Various statements can taken as being either homological or heterological in nature.

A heterological predicate, statement or sentence is one that doesn't apply to itself.

The statement “All truth-claims are relative”, for example, may not (necessarily) be self-applicable.

Alternatively, other statements can be taken as being homological in nature.

A homological statement is one that does apply to itself.

To take statement “All truth-claims are relative” again: that may (or even must) itself be relative to context, utterer, etc.

However, the relativist statement

“All truth-claims are relative.”

the statement

“All theories and statements must be open to possible falsification.”

and

“Every statement must be verifiable or testable in order to be meaningful.”

may all be heterological statements. That is, these statements may not be self-applicable.

Why is that?

Primarily because they can be taken to be second-order (or metalinguistic) statements.

Take the relativist statement again.

That claim may be about (or have) first-order truth-claims in its domain (or in its “object language”) which aren't themselves (generally speaking) about truth-claims themselves. They are about objects, events, happenings, etc. in the world. Of course such second-order (or metalinguistic) statements can themselves be related to the metalinguistic frameworks in which they're stated or even to yet higher-order metalinguistic frameworks.

These meta-statements don't deny that they have the property of being related to frameworks. The statements may concede (as it were) their own necessary status vis-à-vis higher metalinguistic languages. They may also concede that their very own expressions are self-applicable. That is, they may concede (or admit) their own self-referentiality or homologicality.

However, Thomas Nagel, for example, has said that the relativist statement must be a victim of relativity itself if it's taken as true. So what Nagel says about relativism generally can, in effect, be said of the statemental formulation of relativism that's used here. And if that’s the case, then why should we pay it any attention? Though isn’t Nagel assuming:

i) He can escape from relativity himself?

         ii) That relativists deny self-relativity?
        iii) Or, alternatively, that the relativist himself can't escape from relativity?

Not all these possibilities may actually be the case.

Reference

Nagel, Thomas. (1997) The Last Word

Truth: Its Metaphysics, Epistemology and Semantics

We can say that epistemology essentially concerns itself with two things: truth and our “relationship to truth”. Many philosophers, however, would say that truth simpliciter (rather than our knowledge of truth) is a metaphysical (... or a semantic... or a philosophy of language or mind) issue, not primarily one of our knowledge and therefore epistemology.
 

In terms of truth being a metaphysical issue.

This is the case because various philosophers see truth as either some kind of property or even some kind of entity. Not only that: a property that is mind-independent (even if minds can come to know the truth). Strictly speaking, then, truth is a question of ontology, which is a branch of metaphysics.

As for truth being deemed an issue for the philosophy of language.

We can say that this is the case because truth is seen as a property of sentences or statements. Yet even here we smuggle in metaphysics by talking of the properties of statements. What kind of property is that? How does the property truth attach itself to sentences? What is the relation between the statement and its truth-property?

The philosopher of language can circumvent metaphysics by saying that truth is literally a linguistic property, not a metaphysical one. That is, saying that truth is linguistic (or semantic) is a reference to the linguistic fact that we can add the predicate ‘is true’ to the statement “Dolphins are mammals”. Truth is a semantic endorsement of a prior truth-claim or statement. Thus truth- deflationists, for example, argue that we can easily drop the “is true” from the statement without any loss of power or meaning. In that case, the semanticist can simply get rid of truth altogether (as is the case with semantic naturalisers).

Earlier I made the twofold split between truth and our knowledge of truth. We can say, however, that truth must come before our knowledge of truth. Or the metaphysics or semantics of truth must come before epistemology simply because of the fact that we can’t have knowledge of a truth if we don’t already know what truth is. However, we can epistemologise (as it were) truth by arguing that truth is somehow a function of our knowledge of truth (or of the tools and procedures required to discover truth).

A similar manoeuvre can be found in semantics.

Many logical positivists, for example, originally argued that the meaning of a sentence is the means we use to verify it. And verification is an epistemological issue in that we require epistemic tools and procedures in order to verify a statement or proposition. So just as meaning was seen as a function of epistemic verification, we can now argue that the truth of a statement is a question - or function - of the epistemic tools and procedures we require to either construct truth or discover it. And if all we have are such epistemic tools and procedures (i.e., not a property we can call ‘truth’), then we can become truth-deflationists (or truth-naturalisers) by simply getting rid of truth altogether (or, at the least, getting rid of the predicate ‘is true’). Thus we can conclude that naturalised epistemology basically gets rid of the metaphysics of truth.

A Coherent Madman and His Little Self-referential Problem

 

The madman or religious maniac can be entirely coherent and systematic yet also be completely divorced from the world. His system of beliefs may also be entirely self-contained and even self-generated.

Alternatively, his set of beliefs may be based on certain foundational premises, from which his entire system is derived. However, the foundational premises may be utter nonsense even though their implications and entailments are valid (i.e., valid, though not sound).

For example, one such foundational premise may be:

“Every statement in this Holy Book is true.”

Thus not only would he have numerous statements which he could believe (i.e., the ones in his Holy Book); he could also believe all the propositions that are entailed or implied by these statements.

For example, one such statement in the Holy Book could be:

“Accept everything that your heart says is true.”

From this statement he could infer numerous other statements of belief that aren't even directly connected to the original statements he's accepted in the Holy Book itself. However, this could also lead him to reject certain statements in the Holy Book.

For example, his heart may tell him that certain statements in the Holy Book are untrue. He would therefore have a tailor-made system of beliefs which both makes him accept many statements in the Holy Book and yet also allows him to reject the ones he thinks are untrue (or which he simply dislikes).

Then he'd have a problem with self-reference. That is, the Holy Book says of itself:

“Everything in this book is true.”

Though another statement in the Holy Book also says:

“Accept what your heart says is true.”

Which he does. His heart tells him that certain statements in the Holy Book are false. So according to the Holy Book and the man himself, the Holy Book says that everything within it is true and that everything one’s heart says is true. Though the heart says that certain statements in the Holy Book are false. Thus the Holy Book says that everything it says is true; though it also accepts a statement that makes some of its other statements false.

If this man hadn't accepted the foundational statement that “Everything this book says is true”, he wouldn’t have accepted the statement that one should accept what the heart says (i.e., even if it says that certain statements in the Holy Book are false).

We can say that there are two systems now: the man’s and the Holy Book’s. The man’s system grew out of the Holy Book; though the Holy Book allowed him to disregard certain statements within it.

Of course if the Holy Book says that “Everything in this book is true” then that statement itself must also be true. Though, again, the Holy Book contains a statement which allows the possibility that a person needn't accept everything within it.

There is also the self-referential problem of the Holy Book referring to itself. Say that the statement “Everything in this book is true” was said or written at time t¹; though the work itself wasn't finished until time t². Then that statement about the book (which is within the book) was written or said before the book was actually completed. If that's the case, how was it known at time t¹ that everything said or written after would be true if there was no knowledge of such future statements?

There are two answers to this.

One is that although the statement “Everything in this book is true” at the beginning of the book, it mightn't have been written or said until the end of the book. It may be entirely coincidental that the book was compiled with the self-referential statement at the beginning rather than at the end.

Another answer would be that God created the entire book in one go. Therefore it's just a fortuitous that the self-referential statement is at the beginning. In that case, that statement is neither at the end nor the beginning of the book. All statements came together at the same moment in the mind of God. Of course we aren't omniscient like God; therefore our version of the book must contain that statement somewhere in the work: either at the beginning, the end or even in the middle. Again, if God is outside of time, then it makes no sense to say that the statement of self-reference occurs at a particular time within the book. The Holy Book is an abstract object in the mind of God and so it doesn't partake of temporal sequence.

However, isn’t

i) “Everything within this book is true.”

similar to

ii) “Everything within this statement is true.”?

(This is a version of the well-known statement, “This statements is false.”)

However, they're not identical in form. The first sentence (i) seemingly refers to something else – viz., “this book”; whereas the second statement (ii) refers only to itself qua statement. However:

The book the first statement refers to is the book that contains the statement that refers to the book.

So statement (i) is still self-referential; though not entirely so because there are many statements in the book other than “Everything within this book is true”. That statement refers both to itself and every other statement in the book. If the self-referential statement weren't true, then neither would all the other statements in the book be true.

The second statement (ii) above is more clearly self-referential than the first statement. Perhaps it only achieves this because it is without content. It says of itself that everything within itself is true. However, in a certain sense there's nothing within itself. What is this “everything” that's “within” the statement? It quantifies using the term “everything” . Though the only thing that's in the statement (other than the subject-term) is the predicate “is true”. How can the clause “everything within this statement” be true? It's not making a claim about anything other than itself.

Thus

“Everything within this statement is true” is true if and only if everything within statement S is true (its quasi truth conditions).

Thus the statement is true if and only if it is true. It doesn't parallel the form of the T sentence

The sentence ‘Snow is white’ is true iff snow it white.

because here the predicate “is true” refers to the sentence that claims that snow is white. Thus there's a reference to both snow being white and to the sentence which says “Snow is white”. This is unlike the truth predicate in the self-referential statement because this truth predicate applies to both a statement with truth conditions (i.e., snow's being white) and to the metalinguistic sentence that says “The sentence....' is true iff '....”.