Consistency – Maverick Philosopher

Why be Consistent?

Three types of consistency distinguished: logical, pragmatic, and Emersonian.

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Are Fascist Antifa Thugs Blind to their Contradictory Behavior?

A re-titled and redacted version of an entry originally posted 1 September 2017.

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At Berkeley and other universities, protesters have held up signs saying “F–k Free Speech” and have threatened to beat up anyone taking their pictures, including journalists. They seem blissfully ignorant of the contradiction in using fascistic tactics as anti-fascist protesters. After all, a leading definition of fascism is “a tendency toward or actual exercise of strong autocratic or dictatorial control.”

If there is a 'contradiction' involved here it is not logical but practical/pragmatic. In the terminology of the preceding entry, it is not an instance of logical inconsistency, but of inconsistency in the application of a principle or standard. If the principle is "It is wrong to employ fascist tactics," then the practical contradiction consists in the Antifa thugs' application of the principle to their enemies but not to themselves.

But then it dawned on me (thanks to some comments by Malcolm Pollack and 'Jacques' who cannot go by his real name because of the leftist thugs in the academic world) that there is no practical/pragmatic contradiction or double standard here. The Antifa thugs and their ilk operate with a single standard: do whatever it takes to win.

They don't give a rat's ass about consistency of any kind or the related 'bourgeois' values that we conservatives cherish such as truth. These values are nothing but bourgeois ideology the function of which is to legitimate the 'oppressive' institutional structures that the Marxist punks battle against.

When Turley says that the thugs "seem blissfully ignorant of the contradiction" he assumes that they accept the principle but have somehow failed to realize that they are applying it inconsistently. But that is not what is going on here. They don't accept the principle! They have nothing against fascist tactics if they can be employed as means to their destructive ends. But if the political authorities arrest them and punish them, as they must to maintain civil order, then they scream Fascism! and dishonestly invoke the principle.

Besides, they don't accept the meta-principle that one ought to be consistent in the application of principles.

It is a mistake to think that one can reach these people by appealing to some values we all supposedly share. "Don't you see, you are doing the very thing you protest against!" You can't reach these evil-doers in this way. You reach them by enforcing the law. At some point you have to start breaking heads. But that is not 'fascism,' it is law enforcement.

If the authorities abdicate, if the police stand idly by while crimes against persons and property are committed, then they invite a vigilante response. Is that what you want?

The "Fuck Free Speech" signs make it clear that the Antifa thugs do not value what we value. And because they do not share this classically liberal value, it is a mistake to say that they operate with a double standard: Free speech for me, but not for thee. They don't value free speech at all; what they value is winning by any means. If there are times and places where upholding free speech is a means to their ends, then they uphold it. But at times and in places where shutting down free speech is instrumentally useful, then they will shut it down.

It is right out of the Commie playbook. And just as a Nazi is not the cure for a Commie, a Commie is not the cure for a Nazi. The cure for both is an American steeped in American values.

Antifa Thugs Ignorant of Contradiction?

Jonathan Turley:

At Berkeley and other universities, protesters have held up signs saying “F–k Free Speech” and have threatened to beat up anyone taking their pictures, including journalists. They seem blissfully ignorant of the contradiction in using fascistic tactics as anti-fascist protesters. After all, a leading definition of fascism is “a tendency toward or actual exercise of strong autocratic or dictatorial control.”

They don't give a rat's ass about consistency of any kind or the related 'bourgeois' values that we conservatives cherish such a truth. These values are nothing but bourgeois ideology the function of which is to legitimate the 'oppressive' institutional structures that the Marxist punks battle against.

Besides, they don't accept the meta-principle that one ought to be consistent in the application of principles.

If the authorities abdicate, if the police stand idly by while crimes against persons and property are committed, then you invite a vigilante response. Is that what you want?

It is right out of the Commie playbook. And just as a Nazi is not the cure for a Commie, a Commie is not the cure for a Nazi. The cure for both is an American steeped in American values.

Why Be Consistent? Three Types of Consistency

A reader inquires:

This idea of the necessity to be consistent seems to be the logician's "absolute," as though being inconsistent was the most painful accusation one could endure. [. . .] What rule of life says that one must be absolutely consistent in how one evaluates truth? It is good to argue from first principles but it can also lead one down a rat hole.

Before we can discuss whether one ought to be consistent, we need to know which type of consistency is at issue. There are at least three types of consistency that people often confuse and that need to be kept distinct. I'll call them 'logical,' 'pragmatic,' and 'diachronic.' But it doesn't matter how we label them as long as we keep them separate.

1. Logical or Propositional Consistency. To say of two propositions that they are consistent is to to say that they can both be true, where 'can' expresses logical or broadly logical possibility. To say of two propositions that they are inconsistent is to say that they cannot both be true, where 'cannot' expresses logical or broadly logical impossibility.

I am blogging but not wearing a hat. My blogging is obviously consistent with my not wearing a hat since both propositions are true. But my blogging is also consistent with my wearing a hat since it is possible that I both be blogging and wearing a hat. But I am blogging now and I am not writing now are inconsistent since they cannot both be true. The first proposition entails the second, which implies the impossibility of the first being true and the second false.

P1. Human fetuses have a right to life which cannot be overridden except in rare cases (e.g. threat to the life of the mother).

P2. Capital punishment for certain offences is morally justified.

Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)

Ralph Waldo Emerson on the Trumpian ‘Flip-Flop’

Here is a famous passage from Ralph Waldo Emerson's "Self-Reliance" rarely quoted in full:

A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words and tomorrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day. (Ziff, 183)

People routinely rip the initial clause of this passage out of its context and take Emerson to be attacking logical consistency. Or else they quote only the first sentence, or the first two sentences. An example by someone who really ought to know better is provided by Robert Fogelin in his book, Walking the Tightrope of Reason (Oxford UP, 2001). Chapter One, "Why Obey the Laws of Logic?," has among its mottoes (p. 14) the first two sentences of the Emerson quotation above. The other three mottoes, from Whitman, Nietzsche, and Aristotle, are plainly about logical consistency.

The consistency in question is diachronic rather than synchronic. A “little mind” is “foolishly consistent” if it refuses to change its beliefs when change is needed due to changing circumstances, further experience, or clearer thinking. It should be clear that if I believe that p at time t, but believe that ~p at later time t*, then there is no time at which I hold logically inconsistent beliefs.

Doxastic alteration, like alteration in general, is noncontradictory for the simple reason that properties which are contradictory when taken in abstracto are had at different times. My coffee changes from hot to non-hot, and thus has contradictory attributes when we abstract from the time of their instantiation. But since the coffee instantiates them at different times, there is no contradiction such as would cause us to join Parmenides in denying the reality of the changeful world.

Belief change is just a special case of this.

Emerson’s sound point, then, is that one should not make a fetish out of doxastic stasis: there is nothing wrong with being ‘inconsistent’ in the sense of changing one’s beliefs when circumstances change and as one gains in experience and insight. But this is not to say that one should adopt the antics of the flibbertigibbet. Relative stability of views over time is an indicator of character.

Before leaving this topic, let's consider what Walt Whitman has to say in the penultimate section 51 of “Song of Myself” in Leaves of Grass:

Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)

Here it appears that Whitman is thumbing his nose at logical consistency. If so, the Emersonic and Whitmanic dicta ought not be confused. But confuse them is precisely what Fogelin does when he places the Emerson and Whitman quotations cheek-by-jowl on p. 14 of his book.

That being said, Professor Fogelin is a very good philosopher, and the book I refer to above is well worth your time.

The Movies Inside Our Heads

Scott Adams:

As I often tell you, we all live in our own movies inside our heads. Humans did not evolve with the capability to understand their reality because it was not important to survival. Any illusion that keeps us alive long enough to procreate is good enough.

Adams is telling us either directly or by implication that

a. The ability to understand reality is not important to survival.

b. We don't have this ability because we cannot transcend the "movies inside our heads."

c. Knowledge of truth (understanding of reality) is not necessary for procreation; illusions are good enough for procreation.

d. The foregoing propositions are all true.

I will leave it as an exercise for the reader to show that this is an inconsistent tetrad.

Bertrand Russell: Empiricism is Self-Refuting. Is He Right?

An Inquiry into Meaning and Truth (1940), 1969 Pelican ed., pp. 156-157:

I will observe, however, that empiricism, as a theory of knowledge, is self-refuting. For, however it may be formulated, it must involve some general proposition about the dependence of knowledge upon experience; and any such proposition, if true, must have as a consequence that [it] itself cannot be known. While therefore, empiricism may be true, it cannot, if true, be known to be so. This, however, is a large problem.

It is indeed a large problem. But, strictly speaking, is empiricism self-refuting? A self-refuting proposition is one that entails its own falsehood. *All generalizations are false* is self-refuting in this sense. It is either true or not true (false). (Assume Bivalence) If true, then false. If false, then false. So, necessarily false. Other self-refuting propositions are antinomies: if true, then false; if false, then true.

Let empiricism be the proposition, *All knowledge derives from sense experience.* Clearly, this proposition does not refute itself. For it does not entail its own falsehood. It is not the case that if it is true, then it is false. Rather, if it is true, then it cannot be known to be true. For it is not known by experience, and therefore not knowable if true.

Empiricism, then, is not self-refuting, but self-vitiating, self-weakening. It is in this respect like the thesis of relative relativism (RR): it is relatively true that all truths are relative. (RR) does not refute itself, but it does weaken itself. Presumably, what the relativist really wants to say is something stentorian and unqualified: all truths are relative! But the demands of logical consistency force him to relativize his position.

The real problem is that if empiricism is true, then it cannot be believed with justification. For on empiricism the only justificatory grounds are those supplied by sense experience. It is also quite clear that empiricism is not a formal-logical truth or an analytic truth. A logical positivist would have to say it is cognitively meaningless. But we shouldn't go that far. It plainly enjoys cognitive meaning.

You might say that empiricism is just a linguistic proposal, a non-binding suggestion as to how we might use words. Equivalently, one might say it is just a stance one might adopt. If you tell me that, then I will thank you for 'sharing,' but then politely voice my preference for either a non-empirical stance or a stance that is not a mere stance, but the blunt asseveration that empiricism is false. After all, I know that kindness is to be preferred over cruelty, ceteris paribus, and I know this by a non-empirical value intuition.

Another wrinkle is this. If all knowledge derives from sense experience, then presumably this cannot just happen to be the case. I should think that if empiricism is true, then it is necessarily true. But what could be the ground of the necessity? I have already noted, in effect, that the necessity is neither formal-logical nor analytic. Is the necessity grounded in the nature, essence, eidos, of knowledge? That would be a rather unempirical thing to say. Empiricists have no truck with essences or Forms or eide.

Here then we appear to have a further embarrassment for empiricism. It cannot be the nature of knowledge to derive from and have its sole justificatory ground in sense experience. So it just happens to be the case. This cannot be ruled out as logically impossible. But it smacks of deep incoherence and is, shall we say, profoundly unsatisfactory.

Please note that similar reasoning can be deployed against scientism. If all knowledge is natural-scientific knowledge, then this proposition, if true, cannot be known to be true. Is it then merely believed without justification? Is it merely a matter of adopting the 'scientistic stance' or doing the 'scientistic shuffle'? If so, I will thank you for 'sharing' but then politely refuse your invitation to dance.

Hat Tip: I thank Patrick Cronin for reminding me of the Russell passage.

Nothing is Written in Stone

The curiosity to the left, sent to me without commentary by the inscrutable and seldom seen Seldom Seen Slim, raises a number of deep and fascinating questions.

The sentence to the left can be read either literally or metaphorically. My analysis in this entry is concerned with a literal reading only.

1. If nothing is written in stone, then no sentence is written in stone. But the sentence to the left is written in stone. Therefore, it is not the case that nothing is written in stone. Therefore, the sentence to the left, if true, is false. And if it is false, then of course it is false. (Our sentence is not like the Liar sentence which, if true is false, and if false is true.) Therefore, whether the stone sentence is true or false, it is false. Therefore, it is necessarily false, and its negation — 'Something is written in stone' — is necessarily true. (Bivalence is assumed.)

But this is paradoxical! For while it is the case that the sentence is false it could have been true. For it is possible that nothing ever have been written in stone. Therefore, it is not the case that the sentence in question is necessarily false. Something has gone wrong with my analysis. What has gone wrong, I think, is that I have failed to observe a distinction I myself have drawn in earlier entries between propositional self-refutation and performative self-refutation.

2. Consider 'There are no true propositions.' This is a proposition and it is either true or false. If true, then false. And if false, then false. So necessarily false. This is a clear example of propositional self-refutation. The proposition refutes itself by itself. No human act or performance comes into the picture. 'There are no assertions' is quite different. This is either true or false. And we know it is false as a matter of contingent fact. But it is not self-refuting because if it were true it would not follow that it is false. It does not refute itself by itself. For if it were true that there are no assertions, then it would be true that there are no assertions. (Compare: if it were true that that there are no true propositions, then it would be false that there are no true propositions.)

All we can say is that 'There are no assertions,' while it can be asserted, cannot be asserted with truth. For the performance of assertion falsifies it. We thus speak here of performative inconsistency or performative self-refutation. The truth of 'There are no assertions,' if it is true, is assertively inexpressible. It is impossible that I, or anyone, assert, with truth, that there are no assertions; but it it does not follow that it is impossible that there be no assertions.

'I do not exist' is another example of performative self-refutation. I cannot assert, with truth, that I do not exist. For I cannot make the assertion without existing. Indeed, I can't even think the thought *I do not exist* without existing. But the impossibility of my thinking this thought does not entail the necessity of my existence. Necessarily, if I think, then I exist. But the necessity of the consequence does not transfer to the consequent. Both of the following are true and thus logically consistent: I cannot think without existing; I exist contingently. I cannot use the Cartesian cogito to show that I am a necessary being. (Nor can you.)

And similarly with 'Nothing is written in stone' inscribed in stone. The 'performance' of inscribing in stone falsifies the sentence while 'verifying' its negation: if I inscribe in stone 'Something is written in stone,' I provide a concrete instance of the existentially general sentence. (Am I punning on 'concrete'?)

My point, then, is that our lapidary example is not an example of strictly propositional self-refutation but of performative self-refutation where the performance in question is that of inscribing in stone. But why is this so interesting?

3. One reason is that it raises the question of inexpressible propositions. Interpreted literally, though perhaps not charitably, our stone sentence expresses a proposition that cannot be expressed salva veritate in stone. For if we try to express the proposition by producing an inscription in stone, we produce a sentence token whose existence falsifies the proposition. This holds in every possible world. In no world in which nothing is written in stone can this proposition be expressed in stone.

But the proposition expressed by the stone sentence can be expressed salva veritate in speech. Consider a possible world W in which it is literally true that nothing is written in stone, i.e., a world in which there are no stone inscriptions, in any language, of any declarative sentence. If a person in W assertively utters the sentence 'Nothing is written in stone,' he expresses a proposition true in W.

'There are no sayings' cannot be expressed salva veritate in speech but it can be expressed in stone.

I conclude that there are possibly true propositions which, while they are expressible, are not expressible in all media. The proposition expressed by our stone inscription above is true in some possible worlds but not expressible by stone inscriptions in any possible world.

Note also that there are actually true propositions that cannot be expressed in some media. In the actual world there is no ink that is compounded of the blood of Irishmen, 5W30 motor oil, and the urine of my cat, Max Black. So it is actually true that there is no such ink. This truth, however, cannot be expressed in writing that uses the ink in question.

A really interesting question is whether there are true propositions or possibly true propositions that are inexpressible salva veritate in every medium. I mean inexpressible in principle, not inexpressible due to our finite resources.

Buddhists typically say that all is empty and all is impermanent. Could it be true that all is empty despite the fact that this very thesis must be empty and therefore devoid of a determinate sense and a determinate truth value? Could it be true that all is impermanent despite the fact that this very thesis is impermanent?

The MavPhil Doctrine of Abrogation

In cases of 'Emersonian' inconsistency, later entries of this weblog abrogate earlier ones.

For an explanation of 'Emersonian' inconsistency and its difference from logical inconsistency, see On Diachronic or 'Emersonian' Consistency.

On Diachronic or ‘Emersonian’ Consistency

Yesterday I said I was opposed to ". . . misquotation, misattribution, the retailing of unsourced quotations, the passing off of unchecked second-hand quotations, and sense-altering context suppression." An example of the last-mentioned follows.

Here is a famous passage from Ralph Waldo Emerson's "Self-Reliance" rarely quoted in full:

A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and
divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words and tomorrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day. (Ziff, 183)

It should be clear to anyone who reads the entire passage quoted above in the context of Emerson's essay that Emerson’s dictum has nothing to do with logical consistency and everything to do with consistency of beliefs over time. The consistency in question is diachronic rather than synchronic. A “little mind” is “foolishly consistent” if it refuses to change its beliefs when change is needed due to changing circumstances, further experience, or clearer thinking. It should be clear that if I believe that p at time t, but believe that ~p at later time t*, then there is no time at which I hold logically inconsistent beliefs. Doxastic alteration, like alteration in general, is noncontradictory for the simple reason that properties which are contradictory when taken in abstracto are had at different times. My coffee changes from hot to non-hot, and thus has contradictory attributes when we abstract from the time of their instantiation. But since the coffee instantiates them at different times, there is no contradiction such as would cause us to join Parmenides in denying the reality of the changeful world.

Belief change is just a special case of this. Suppose a politician changes her position for some good reason. There is not only nothing wrong with this, it shows an admirable openness. She goes from believing in a progressive tax scheme to believing in a flat tax, say. Surely there is no logical contradiction involved, and for two reasons.

First, the property of believing that a progressive tax is warranted is not the contradictory, but merely the contrary, of the property of believing that a flat tax is warranted. (They cannot both be instantiated at the same time, but it is possible that neither be instantiated.) Second, the properties are had at different times. A logical contradiction ensues only when one simultaneously maintains both that p and that ~p.

Before leaving this topic, let's consider what Walt Whitman has to say in the penultimate section 51 of “Song of Myself” in Leaves of Grass:

Do I contradict myself? Very well then I contradict myself, (I am large, I contain multitudes.)

Nick Gillespie on Why Youth Favor Obama and Conservatism’s Contradictions

Support for Obama among 18-29 year olds exceeds that of any other age cohort. Reason Magazine's Nick Gillespie argues that Obama is in the process of "screwing them big time." Gillespie is right. What caught my eye, however, was Gillespie's explanation of why conservatives fail to get the youth vote:

I'd argue that what makes "the conservative message" resonate less among younger people is its, well, conservatism on things such as war, alternative lifestlyes, [sic] drug legalization, and immigration. Younger people are less hung up on the sorts of things that really twist conservatives' knickers. And young people then assume that many of the other things that conservatives espouse – such as generally free markets and open trade – are similarly warped. That conservatives are so inconsistent with their basic message – We want smaller government…except when we're talking about immigrants, the gays, and the ability to kill people overseas! – doesn't help matters, either. Most people surely don't prize consistency as much as libertarians do, but the obvious contradictions at the heart of conservative philosophy are off-putting to anyone with the smallest taste for consistency.

As a philosopher, logical consistency looms large for me. And so you will get my attention 'big time' if you can lay out for me "the obvious contradictions at the heart of conservative philosophy." But if they are obvious, then presumably all you need to do is draw my attention to them.

Unfortunately, public intellectuals, not being logically trained as most philosophers are, have an egregiously spongy notion of what a contradiction is. This is true of even very good public intellectuals such as Nat Hentoff and Nick Gillespie. (Hentoff, for whom I have a very high degree of respect, thinks one is being inconsistent if one is pro-life and yet supports capital punishment. He is demonstrably wrong.)

Ignoring Gillespie's invective and hyperbole, his point seems to be that the following propositions are logically inconsistent:

1. The legitimate functions of government are limited.

2. Among the the legitimate functions of government are national defense, securing of the borders, and preservation of traditional marriage's privileged position.

Now it should be obvious that these propositions are logically consistent: they can both be true. They are not logical contradictories of each other.

It is therefore foolish for Gillespie to accuse conservatives of inconsistency. And to speak of obvious inconsistency is doubly foolish. What he needs to do is argue that the governmental functions that conservatives deem necessary and legitimate are neither. This will require a good deal of substantive argumentation and not a cheap accusation of 'inconsistency.' For example, he can mount an economic argument for open borders. I wish him the best of luck with that. He will need it.

Curiously, Gillespie's own reasoning can be used against him. Suppose an anarchist comes along. Using Gillespie's own form of reasoning, he could argue that Gillespie the libertarian is being inconsistent. For he wants smaller government . . . except when it comes to the protection of life, liberty, and property (the Lockean triad, I call it). Then he wants coercive government to do its thing and come down hard on the malefactors. He's inconsistent! If he were consistent in his desire for limited government, he would favor no government. His libertarianism would then collapse into anarchism.

So by his own understanding of consistency, Gillespie is not being consistent. The same reasoning that he uses against conservatives can be used against him. The reasoning is of course invalid in both applications. It is invalid against the libertarian and equally so against the conservative.

But I like his black leather jacket schtick. It is always a pleasure to see him on the O'Reilly Factor.

On the Obvious

As Hilary Putnam once said, "It ain't obvious what's obvious." Or as I like to say, "One man's datum is another man's theory."

But is it obvious that it ain't obvious what's obvious?

It looks as if we have a little self-referential puzzle going here. Does the Hilarian dictum apply to itself? An absence of the particular quantifier may be read as a tacit endorsement of the universal quantifier. Now if it is never obvious what is obvious, then we have self-reference and the Hilarian dictum by its own say-so is not obvious.

Is there a logical problem here? I don't think so. With no breach of logical consistency one can maintain that it is never obvious what is obvious, as long as one does not exempt one's very thesis. In this case the self-referentiality issues not in self-refutation but in self-vitiation. The Hilarian dictum is a self-weakening thesis. Over the years I have given many examples of this. (But I am now too lazy to dig them out of my vast archives.)

There is no logical problem, but there is a factual problem. Surely some propositions are obviously true. Having toked on a good cigar in its end game, when a cigar is at its most nasty and rasty, I am am feeling mighty fine long about now. My feeling of elation, just as such, taken in its phenomenological quiddity, under epoche of all transcendent positings — this quale is obvious if anything is.

So let us modify the Hilarian dictum to bring it in line with the truth.

In philosophy, appeals to what is obvious, or self-evident, or plain to gesundes Menschenverstand, et cetera und so weiter are usually unavailing for purposes of convincing one's interlocutor.

And yet we must take some things as given and non-negotiable. Welcome to the human epistemic predicament.

Collective Inconsistency and Plural Predication

We often say things like

1. The propositions p, q, r are inconsistent.

Suppose, to keep things simple, that each of the three propositions is self-consistent. It will then be false that each proposition is self-inconsistent. (1), then, is a plural predication that cannot be given a distributive paraphrase. What (1) says is that the three propositions are collectively inconsistent. This suggests to many of us that there must be some one single entity that is the bearer of the inconsistency. For if the inconsistency does not attach distributively to each of p, q, and r, then it attaches to something distinct from them of which they are members. But what could that be?

If you say that it is the set {p, q, r} that is inconsistent, then the response will be that a set is not the sort of entity that can be either consistent or inconsistent. Note that it is not helpful to say

A set is consistent (inconsistent) iff its members are consistent (inconsistent).

For that leaves us with the problem of the proper parsing of the right-hand side, which is the problem with which we started.

And the same goes for the mereological sum (p + q + r). A sum or fusion is not the sort of entity that can be either consistent or inconsistent.

What about the conjunction p & q & r? A conjunction of propositions is itself a proposition. (A set of propositions is not itself a proposition.) This seems to do the trick. We can parse (1) as

2. The conjunctive proposition p & q & r is (self)-inconsistent.

In this way we avoid construing (1) as an irreducibly plural predication. For we now have a single entity that can serve as the logical subject of the predicate ' . . . is/are inconsistent.' We can avoid saying, at least in this case, something that strikes me as only marginally intelligible, namely, that there are irreducible monadic non-distributive predicates. My problem with irreducibly plural predication is that I don't know what it means to say of some things that they are F if that doesn't mean one of the following: (i) each of the things is F; (ii) there is a single 'collective entity' that is F; or (iii) the predicate 'is F' is really relational.

One could conceivably object that in the move from (1) to (2) I have 'changed the subject.' (1) predicates inconsistency of some propositions, while (2) predicates (self)-inconsistency of a single conjunctive proposition. Does this amount to a changing of thr subject? Does (2) say something different about something different?

Five Grades of Self-Referential Inconsistency: Towards a Taxonomy

Some sentences, whether or not they are about other things, are about themselves. They refer to themselves. Hence we say they are 'self-referential.' The phenomenon of sentential self-referentiality is sometimes benign. One example is 'This sentence is true.' Another is 'Every proposition is either true or false.' Of interest here are the more or less malignant forms of self-reference. One example is the so-called Liar sentence:

1. This sentence is false.

If (1) is true, then it is false, and if false, then true. This is an example of an antinomy. In pursuit of a taxonomy, we might call this Grade I of self-referential inconsistency. Grade I, then, is the class
of self-referentially inconsistent sentences that issue in antinomies.

There are other self-referential sentences that are not antinomies, but imply their own necessary falsehood. These are such that, if true, then false, and if false, then false, and are therefore necessarily false. For example,

2. All generalizations are false.

If (2) is true, then, since (2) is itself a generalization, (2) is false. But its falsity does not imply its truth. So, if false, then false. Assuming Bivalence, it follows that (2) is necessarily false, whence it follows that its negation — Some generalizations are true – is necessarily true, and moreover an instance of itself. A second example might be

3. There are no truths.

If (3) is true, then it is false. And if false, then false. So, (3) is necessarily false, whence it follows that its negation — There are truths — is necessarily true.

Examples (2) and (3) belong to Grade II in my tentative taxonomy. These are self-referential sentences that entail their own necessary falsehood. Grade III comprises those self-referential sentences that are such that if true, then neither true nor false, and if false, then false. For example,

4. There are no truth-bearers.

If (4) is true, then, since (4) is a truth-bearer, (4) is neither true nor false. But if false, then false. If we define the cognitively meaningful as that which is either true or false, then (4) is either cognitively meaningless or false. A more interesting example that seems to belong in Grade III is the Verifiability Principle of the Logical Positivists:

5. Every cognitively meaningful sentence is either analytic or empirically verifiable in principle.

If (5) is supposed to be cognitively (as opposed to emotionally) meaningful, and thus not a mere linguistic recommendation or pure stipulation, then it applies to itself. So if (5) is true, then (5) —
which is clearly neither analytic nor verifiable — is meaningless. So, if true, then meaningless, and if false, then false. Therefore, either meaningless or false. Not good!

Grade IV comprises those self-referential sentences that can be described as self-vitiating (self-weakening) though they are not strictly self-refuting. For example,

6. All truths are relative.

If (6) is true, then (6) is relative, i.e., relatively true. It is not the case that if (6) is true, then (6) is false. So (6) is not self-refuting. Nevertheless, (6) is self-vitiating in that it relativizes and thus weakens itself: if true, it cannot be absolutely true; it can only be relatively true. It is therefore a mistake, one often made, to say that he who affirms (6) contradicts himself. He does not. He would contradict himself only if he maintained that it is nonrelatively true that all truths are relative. But no sophisticated relativist would say such a thing. Other examples which seem to fall into the category of the self-vitiating:

7. Every statement is subject to revision. (Quine)
8. Every theory reflects class interests. (Marxism)
9. All theory is ideology. (Marxism)
10. Nothing can be known.
11. Nothing is known.
12. Nothing is certain.
13. All truth is historical.
14. All is opinion.

What is wrong with self-vitiating propositions? What does their weakness consist in? Consider (8). If (8) is true, then the theory that every theory reflects class interests itself reflects class interests. Suppose (8) reflects the class interests of the proletariat. Then what is that to me, who am not a proletarian? What is it to anyone who is not a proletarian? If (8) is true only for you and those with your interests, and your interests are not my interests, then I have been given no reason to modify my views. The trouble with (7)-(14) and their ilk is that they make a claim on our rational attention, on our common rational interest, while undercutting that very claim.

It seems we need a fifth category. The sentences of Grade V are such that, if they are true then they are, not false, and not self-vitiating, but non-assertible. Consider

15. No statement is negative.

(15) applies to itself and so at first appears to refute itself: if (15) is true, then it is false. And if false, then false; hence necessarily false. But consider a possible world W in which God destroys all negative statements and makes it impossible for anyone to make a negative statement. In W, (15) is true, but non-assertible. (15) does not prove itself to be false; it proves itself to be non-assertible.

Can the same said of

16. All is empty (Buddhism)?

I think not, for reasons supplied here.

Finally, we consider

17. All memory reports are deceptive.

This is subject to the retort that one who asserts (17) must rely on memory, and so must presuppose the reliability of the faculty whose reliability he questions by asserting (17). For if anyone is to be in a position responsibly to affirm (17), to affirm it with a chance of its being true, he must remember that on some occasions he has misremembered. He must remember and remember correctly that some of his memories were merely apparent. It seems obvious, then, that the truth of (17) is inconsistent with its correctly being affirmed as true. If true, it is unaffirmable as true. But this is different from saying that (17), if true, is false. Although (17) is unaffirmable or non-assertible if true, it seems that (17) could be true nonetheless.

A Question About Self-Referential Inconsistency

From the mail bag:

I’m hoping you can help me with an annoying question that came up in conversation recently. I’m sure you can answer it much better than me.

Statements are self-refuting when they are included in their own field of reference and fail to conform to their own criteria of validity. Thus ‘there are no truths’ is self-refuting because if it is false, then it is false. But if it is true, then it is false as well because then there would be no truths, including the statement itself. So what about the statement ‘all statements are self-refuting’?

You are right about 'There are no truths.' If true, then false. If false, then false. So necessarily false. Therefore, its negation — 'There are some truths' — is not just true, but necessarily true.

There is exactly the same pattern with 'All statements are self-refuting.' If true, then self-refuting and false. If false, then false. So necessarily false. Therefore, its negation — Some statements are not self-refuting — is not just true, but necessarily true.

Now an intriguing question arises. Are these necessities unconditional, or do they rest upon a condition? The second necessity appears to be conditional upon the existence of statements and the beings who make them. Statements don't 'hang in the air'; a statement is the statement of a stater, so that, in a world without rational beings, there are no statements. 'Some statements are not self-refuting,' therefore, is not true in all possible worlds, but only in those worlds in which statements are made. Given that there are statements, it is necessarily true that some statements are not self-refuting. But there might not have been any statements. The existence of statements is contingent.

Now what about 'There are some truths?' Clearly, this sentence (or rather the proposition it expresses) is not contingently true, but necessarily true. But is it true of absolute metaphysical necessity, or does its necessary truth rest on some condition? Suppose something gives the following little speech:

I see your point. There have to be truths. Forif you say that there aren't any, you are saying that it is true that there aren't any, and you thereby contradict yourself. So there is a sense in which there cannot not be truths. But all this means is that WE must presuppose truth. It doesn't mean that there are truths independently of us. WE cannot help but assume that there are truths. The existence of truths is a transcendental presupposition of our kind of thinking. But it does not follow that there are truths of absolute metaphysical necessity. If we were not to exist, then there would be no truths, not even the truth that we do not exist.

Is the little speech coherent? The objector is inviting us to consider the possible situation in which beings like us do not exist and no truths either. The claim that this situation is possible, however, is equivalent to the claim that it is true that this situation is possible. But, on the transcendental hypothesis in question, the existence of this truth is relative to our existence, which implies that it is not true independently of us that it is possible that beings like us not exist and no truths either. But then it is not really possible that beings like us not exist and no truths either: the possibility exists only relative to our thinking. So I conclude that the transcendental hypothesis is only apparently coherent, and that 'There are truths' is true of absolute metaphysical necessity. So it is not just that we cannot deny truth; truth is undeniable an sich.