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 '....”.

Is Consciousness the Brain Carrying Out Computations?

 

Hilary Putnam once held the position (i.e., in the 1960s) that consciousness is literally the brain computing. That also had the implication (for some people) that it's not necessarily the brain that causes consciousness: it's computation itself. This is the case even if it's computation of a particular kind (in conjunction with its physical or biological implementation) that's required for consciousness. Thus it followed from this, according to Putnam, that if computation is everything, then consciousness can occur in a computer or even in Putnam's own “brain in a vat”. Again, what matters are the computations, not the physical basis of those computations. (To be accurate, in his 1967 paper, Putnam hardly refers to consciousness as such. He talks about “mental states”.)

Daniel Dennett also argued that the computations of the brain are consciousness. This doesn't mean that such brain computations result in consciousness in some kind of causal and temporal sequence. It means that when the brain's computations occur, so too do conscious events. They're one and the same thing. Or, as Dennett himself puts it, it's not a case of brain computations occurring (in what he calls the “Cartesian Theatre”) and then we become conscious of those computations. Instead, when brain-computations occur they actually constitute consciousness. When the brain computes: that's what consciousness is. That's what we're aware of when we're conscious; though we aren't necessarily aware of them as computations (or as anything).

This is similar to John Searle's view in which he says that there's no causal and temporal sequence from a brain state to a mental state in that the mental state is the brain state. The brain state and mental state occur at one and the same time. It isn't a case of brain state at time t¹ causing mental state at time t². Both the brain state and the mental state occur at t¹.

The mental state is the state as experienced from the inside (as it were); whereas the brain state could (in theory at least) be observed by neuroscientists. However, it need hardly be said that Searle doesn't believe that this has anything to do with computations (as such). In his case, it's a point about the (causal) relations between the brain and consciousness; not between computations and consciousness.

Finally, it needn't be the case that consciousness is always (or at all) computation. We can substitute all the references to 'computation' in the above with the words 'brain event' or 'brain state'; as Putnam himself did in his paper of 1967.

References

Dennett, Daniel. (1991) 'The Cartesian Theater and “Filling In” the Stream of Consciousness'.

Putnam, Hilary. (1967) 'The nature of mental states', in Mind Language and Reality: Philosophical Papers, Volume 2.
Searle, John. (1997) The Mystery of Consciousness.

Holisms (3) – Definitional Holism

One

A definition isn't just an appendage to the word under scrutiny. The word would have no meaning if it weren't for the definitions we supply in order to facilitate understanding.

A word isn't atomic in nature. We can't say, for instance, that the word ‘freedom’ means, well, freedom and leave it there. Neither can we accept (on a naturalistic reading) some kind of abstract and non-individuated meaning or proposition which would allow us to escape from our linguistic system. Even if we were to allow for abstract and non-spatiotemporal meanings or propositions, they would still become material or concrete (as it were) as soon as they were expressed and communicated – which would need to be done, evidently, in some natural language or other.

Two

It seems counterintuitive, at least initially, to think that the primary relation is not between words and things, but between words and other words. This isn't so surprising when, for example, we think of the classic example of defining ‘bachelor’ as ‘unmarried man’. However, these words are taken to be synonyms. But try explaining or defining a word like ‘freedom’ again. This certainly doesn't have a reference in a strict sense of the term. Thus we are moved on, immediately, to words like ‘liberty’, ‘choice’, ‘will’ and so on. And try getting further without bringing in terms which are themselves as much in need of defining or explaining as the original word ‘freedom’. Of course it may be the case that we arrive back at the word ‘freedom’ or use this term as part of some of the other definitions.

This word isn't as problematic as words like ‘thing’ and ‘experience’. Try defining those words without reference to things or experience.

It may follow, then, that if a word has a definition which includes terms themselves not defined (or even if we provide simple synonyms for the definiendum) then the speakers may not fully understand the word’s meaning. They may not even understand their own usages of the word in question because any full meaning (or full understanding) can only belong to the linguistic system itself. Any definition or explication of a word's meaning must reach an arbitrary finishing point if the game of understanding is to begin in the first place. And that stopping place will be contingent, if not exactly arbitrary.

Three

Words are defined by other words, which are themselves defined by other words. No word, concept or thing is ever captured in a “finite web” of meaning. This is Karl Popper on this problem:

“The derivation [of a term] shifts the problem of truth back to the premises, the definition shifts the problem of meaning back to the defining terms (i.e., the terms that make up the defining formula). But these, for many reasons, are likely to be just as vague and confusing as the terms we started with, and in any case, we should have to go on to define them in turn; which leads to new terms which too must be defined. And so on, to infinity.”

That must surely be the problem with definitions: they too will contain terms which themselves will need defining.

A similar problem is apparent when it comes to a logical argument and the premises on which it is based. That is, the premises of any argument may themselves depend on further premises and conclusions that may act as justifications for the validity or truth of the initial premise. Thus we have on our hands a regress of justification. However, the game can't go on forever.

This is why we must, at some point, simply accept premises, arguments or definitions if we're to get going on our philosophical or logical enterprise. The premises that we accept, however, needn't be seen as being “self-evident”, “indubitable” or anything like that. They simply need to be the starting points of reasoning if we are to avoid an infinite regress.

In a sense, it's precisely because definitions depend on their own un-defined terms that all words (or nearly all words) are inherently somewhat vague. That's because the meaning of a single word can be said to depend upon all the meanings of all the words in the symbol-system to which it belongs. We can't have a precise definition if the definiendum itself contains terms that aren't themselves defined. Though even if we do in fact define the terms in the definition, these definitions will themselves require elaboration and definition. And so on indefinitely.

The holist position on this problem will be that we must take into account the symbol-system to which the words under definition belong. But this too is problematic. How can we really take on board an entire symbol-system each time we want to define a term? Does this mean going on an infinite regress? Or if not an infinite regress, does it mean taking on board all the other words in a symbol-system? (Or perhaps a large sub-system of the larger system?) So, in that respect, the regress won't be infinite: it will be circular. This essentially means that we will arrive back at some of the terms which we actually started with.

This means that there are jut as many problems with holism (or coherentism) as there are with atomism.

Similar points to those above were raised by, amongst others, Bradley in the 19th century. Because of the problem of holism, Bradley concluded that no statement could be entirely/absolutely true. Similarly, we may now say that no definition is ever free from vagueness precisely because of its containment within a larger symbol-system.