Archive for the ‘Uncategorized’ Category

NYU imperatives workshop

March 21, 2016

Do scientists from differing disciplines have the same goals in addressing the same facts? Linguists attempt to accommodate all the natural language intuitions in their theoretical frameworks. That may lead them to extralogical means. Logicians have often taken on one or another natural language intuition and attempt to augment the logic to accommodate that intuition. In both cases there’s a question of purview: why not accommodate all the intuitions through the logical system, or how much of logic should accommodate the intuitions?

This became the battle at a workshop on imperatives at NYU today. Craige Roberts incorporated pragmatics into her analysis of imperatives to include a wide variety of natural language intuitions, while Kit Fine and Peter Vranas developed new logics to deal with some, but not all, intuitions. They both seemed to ignore that traditional logics are not just inadequate for linguistic intuitions, but also inadequate to basic facts about reality. If we assume that development of logics is still in its infancy, the attempt to accommodate each outstanding challenge is a step towards a more inclusive, flexible and useful logic.

Think of Kratzer’s lumps of thought. She observed that a single event can be represented in multiple descriptions that in sentential logic would imply multiple events, or if not implied, then at least failed to imply that that the descriptions were of the same event: if Sally made a painting that was a portrait depicting her sister, sentential logic would imply three events (or at least not imply one event) “Sally made a painting and painted a portrait and painted a picture of her sister.” That these three descriptions are of one event is not a linguistic intuition, it’s a fact of what Sally did. To formulate a logic that can identify these conjuncts as three descriptions of one event would be progress for logic, not for linguistics.

So it seems to me, logic is justified in picking its challenges independent of the needs of linguistics. The real test would be between AI and neurolinguistics — how are imperatives represented in the brain, how can they best be represented in a robotic program? I didn’t see anything from the linguists giving a brain representation argument the way, say, Chomsky did with syntax. There doesn’t seem to be an experimental program to follow, as there was with generative syntax. The logicians, on the other hand, were always mindful of the algorithmic value of their logic, but that’s why they are logicians.

There was also an interesting exchange on whether the background conditions of an imperative are factual or relative to the speaker or addressee. So “if it’s raining, take an umbrella” can be evaluated on whether it’s actually raining or whether the speaker thinks it’s raining. Does it matter whether it’s actually raining for the force of the imperative to hold? Roberts, the linguist, wants it to be contextual information of the speaker; Vranas wants to take this as factual so that the entailments can be validated within his three-valued logic. At first they seem to be different views — why should it matter whether it’s actually raining, since the imperative is the speaker’s insistence. But if there are only beliefs, and no facts, both views are the same. The force of the imperative, shared by the speaker’s intention and the addressee’s understanding of it, will shift if she comes to believe that it’s not actually raining.

The two talked past each other for about an hour. The problem is a really tough one. The entailments of speakers’ assertions are trivial. Sally said “I’m lying” just in case she said it. So as an assertion, it’s true. But the content, indexed to a speaker, is a paradox. It’s worth remembering that three-valued logic began with an attempt to incorporate the epistemic into the logic. The result is a loss of a distinction between the factual and the epistemic. But there’s an underlying problem: no one knows what is factual; all we know are our beliefs. Deductions from our beliefs will always be trivial; deductions from facts will require extralogical overlays for the epistemic. I worked out the problem a few years back here. I’ve complained that trivalence flattens modality here.


Bossy jerk

February 9, 2016

Sheryl Sandberg, Corporate Operations Officer of Facebook, has created a Ban Bossy campaign to encourage girls to be leaders. Many celebrities have expressed support for the campaign and even advertisers have taken up the cause as a means to market to women.


Sandberg makes several distinct claims about the use and meaning of “bossy.” Some have merit, others are misleading. All of them are fruitful for understanding cultural roles, inequalities, and how they play into perception, attitude and emotional response. I want to take them separately and look at some data.


  • “bossy” is used more to describe females than for males
  • this disparity shows an inequality in our cultural stereotypes
  • cultural stereotypes influence our perception of behavior and our emotional response to behavior
  • the cultural role of boss is masculine so males can’t effectively be disparaged by “bossy”
  • the cultural feminine roles include nurturing roles, not boss roles, so females playing the boss role are perceived as inappropriate
  • the cultural masculine roles include boss, so when men abuse their authority or are pushy or bossy, their behavior is accepted as a norm

Evidence supports some of these claims but not others. A linguistic analysis leads to a more complex relationship between cultural roles/stereotypes/expectations and human attitudes/perceptions/emotional responses that may be independent of the culture. I’m using a beautiful data mine developed by Ben Schmidt. It mines Rate My Professor, an online website that allows students to review their professors. since the professor’s name is identified, the reviews can be sorted by professor’s sex, give or take a few ambiguous names. Professors are quintessential authorities, the reviews are perfectly suited to an understanding of the use and frequency of words like “bossy.”


First, the data clearly show that “bossy” is used more often for female profs than for male ones, although it is used substantially for male professors too. Does this imply that female professors are perceived as bossier than males? That is the Ban Bossy claim — women are rejected in positions of authority. A quick look at “jerk” seems to refute that claim.

“Jerk” is used exclusively for males and it appears in the corpus far more frequently than “bossy” — something like 35 times more frequently. That’s not a little. It’s a huge difference. Are there other negative epithets that might be used for women that are more frequent than “bossy”?

“Mean” is also used more frequently for females than for males. Does this support the Ban Bossy view?

The distribution of “jerk” implies that our language has gendered epithets. “Jerk” is for males, “bossy” for females. If that’s so, then the reason “bossy” is used more for females than for males implies nothing about the emotional response to female roles. It’s used more often because “jerk” is the preferred epithet for males.

The data actually show the opposite of the Ban Bossy view of emotional response to female/male role or expectation. Students object to male authority frequently, possibly more frequently than female authorities. The greater frequency of “mean” for females shows the same: why describe a male as “mean” when there are so many more, and more expressive, epithets for men, including not just “jerk” but “dick,” “douche,” “dickhead,” “prick,” “douchebag,” “son-of-a-bitch,” “bastard” and the declining “schmuck.” Rate My Professor no longer allows the most common epithet for males, “asshole,” but the data mine provides partial data — I assume that Rate My Professor closed below-the-belt epithets shortly after they appeared.

Couple of points here. The wealth of epithets for men imply that in our culture we freely object to male abuse of authority. It’s enshrined in the language. The frequency of their use demonstrates that we object to male abuse of authority. So the differential use of “bossy” is purely linguistic fact, not a fact about our perceptions influencing emotional response. We dislike abuse of authority whether the authority is male or female.

The data also show that our language is gendered. There seem to be many more epithets for male abuse of authority than for females, which does very much correlate with the social fact that men are mostly bosses, or that through the development of our language, bosses were mostly men.

Notice that both “bossy” and “mean” are not particularly gendered in themselves and are literally descriptive and not either metaphorical or metonymic. All the vulgar male epithets are metaphorical or metonymic or both: they refer to taboo body parts some of which metaphorically relate to acts of sexual violence, or they relate metaphorically to the social stigma of illegitimacy. In the context of Rate My Professor, “bossy” and “mean” may indicate a second choice after “bitch” which RMP will not accept as a review. Not exactly a euphemism, but a kind of nonce euphemism.

More important, there are many negative words for females, but they do not cover the abuse of authority. Several include “dits,” “airhead,” “twit” (used for both females and males), “bimbo.” I compare these with cultural female/male attire: pockets are the characteristic of male attire; not only are pants and jackets full of pockets and dresses, skirts and blouses largely devoid of them, but taking a minimal pair — men’s jeans and women’s jeans — you’ll find that women’s jeans’ pockets are often shallow and useless, whereas mens’ are deep and many. Pockets are utilitarian in the sense of of managing the outside world through tools. Pockets hold those tools. Womens’ wear is designed for attractiveness (whether for the male gaze or otherwise), not any other utility besides covering and warmth, and often inadequate for both of those.

Putting the attire next to the epithets a pattern emerges. The cultural roles for men are ones of control and manipulation of the world including other people. The response to their aggressive control is a wealth of epithets that object to male power. The cultural roles for women include aesthetic appeal. The negative epithets might be described as “pretty but useless.”

It seems to me important that the responses to authority in RMP shows that our attitudes towards these cultural roles do not numb our emotions. Any expectation that the boss will be male does not incline us to accept the abuse of authority or prevent us from objecting to it in the strongest terms. So we can distinguish between the cultural roles and the perceptions of them. The data implies to me that culture does not determine thought, it just gives us different ways to express our thoughts depending on cultural categories.

The Ban Bossy campaign has given us an important avenue of research to discover

a. the cultural roles embedded in our language

b. the independence of our responses to those roles

The feminist agenda is a fruitful lens with which to investigate not just the facts of our society — inequities of pay and power — but also of culture and attitude in our language and our perceptions.

Part II — Questions for further research

A more disturbing fact in the data is the disparity in use of “brilliant” and “genius.” These are not gendered words, yet they are used to describe males more frequently than for females, and “genius,” the more hyperbolic word is even more biased towards men than “brilliant.” Assuming that females are at least as bright as men if not brighter, how do we account for this disparity in perception?

In this case, I speculate that this is not a linguistic fact but a behavioral and perceptual reflex — exactly the opposite of the “bossy” analysis which is merely about the lack of available gendered words for female abuse of authority. If males are brought up in our culture to be special, competitive and superior, while females are brought up to be servants — the nurturer, the mother who serves her children,m the caretaker — it would be no surprise if the male instructor in class would present himself as special, competitive with his ideas and superior, while the female instructor would be focused on the students.


Intended paradox

June 16, 2013

“I’m very witty!” someone wrote in a comment box in response to the criticism “You have no wit.”

“I’m very witty” might seem at first a witless and therefore unpersuasive response, unless it is sarcastic, in which case it is actually witty. If it’s sarcastic, the meaning intended to convey is that author isn’t witty, and therefore it implies that the comment itself also is not witty. The joke is, the author knows it’s not witty; yet that’s what makes it witty. So if it’s witty, it’s a lie; if it’s a lie, it’s not witty: a liar paradox.
But if the comment is merely false, then there’s no paradox — just a reply by someone who thinks he’s witty but is too dull to know he’s not witty, and hasn’t enough wit to say so wittily.
So if it’s a lie, then it is a meta-witty paradox; if an honest falsehood, it’s just stupid.

What’s interesting is that the intention or speaker’s attitude or character of mind induces the paradox, not the words alone. The paradox depends on who’s speaking, liar or dolt, wit or fool.

At what price?

June 7, 2013

It’s supposed to be well-established that commodity prices are the inverse of interest rates. Interest rates are as low as they can be and luxury housing prices in NYC are high, for example, and the stock market is flying too. But the rest of the economy is not wildly inflated. Why?

Easy money (low interest rates) flows into commodity inventories (we saw that leading up to the Arab Spring), on the one hand, and on the other, it curbs extraction of new resources and commodities because the low interest rates reduce their monetization, or so the theory goes. Yves Smith posted on it back in 2008:
Here are the originals:

That easy money/low interest rates leads to inflation has been orthodoxy since Friedman at least. It was Volcker’s successful program to curb inflation by increasing interest rates, causing a recession, and Bernanke’s opposite strategy to take us out of recession, allowing inflation. But it also has a specific reflex in commodity prices. QE2 caused a global price hike in food prices as investors left the dollar for commodities, that caused the Arab Spring. Not exactly what Bernanke anticipated. His response was washing his hands: other nations have to deal with their own inflation, he quipped, cynically, I thought.


May 30, 2012

In the latest New Yorker Steven Pinker quotes his defense of the dictionary, “it is not just a matter of opinion that there is no such word misunderestimate, that the citizens of modern Greece are Greeks and not Grecians, and that divisive policies Balkanize rather than vulcanize societies.” Given that language is always in flux, on what principled ground can these be judged? Misunderestimate is redundant, but what of it? Language is full of redundancy, and if some underestimations are benign then maybe misunderestimating is not exactly redundant. If Grecians becomes current, then Greeks will be an anachronism; same with vulcanize. Stranger things have happened to English.

So what’s the purpose of a dictionary? Shouldn’t it be a source of scholarly information — about who uses Balkanize, vulcanize, Grecians and misunderestimating and why, and how their use came to be?  When did scholarly information include prescriptions on use? Shouldn’t that be left to the newly informed reader?

Whether you choose to avoid the intensified “same exact” for fear of someone (as another letter-writer in the same exact issue of the New Yorker) thinking that you are unthinking, that’s a choice you make between using language as if it were logical and systematic (which it can and maybe should be at points) rather than expressive (which it can and should be too). Most such complaints against illogical use are little more than gotcha‘s to show ones linguistic or logical accuity, which though admirable for its accuity is at least as deplorable for its smug, nit-pickity derisiveness.

After all, aint has its place for effective use and so has “Have you finished your homework, yet?” (also from that same letter-writer J.A.F.Hopkins — note the many names). I monitor my own use, but I have garnered not a few enemies for it. Not everyone loves a pedant, and some resent them deeply.

I do not embrace loss of linguistic distinctions. I regularly hear “it begs the question” meaning the uninteresting “it leads to another question,” and it’s been years since I’ve heard anyone use “beg the question” in its old sense of “that’s not an answer but a circuitous restatement of the problem” which was always such a clever rebuttal. But before I’d conclude that English is dying, I’d want to understand better exactly why the changes occur. In this case, it is not that speakers are losing the ability to recognize empty circular reasoning. Begging the question was a rare form belonging to philosophical discourse. The change has not been a loss of the expression, but a popularization. People outside of philosophy are using it, and they use it for their purpose. Within the philosophical community, the expression still thrives exactly as it was and no doubt with the same frequency.

Language is an accommodation to communication for the interchange of information and socialization. That’s what’s interesting in language — not that the language is abused, but why, what conditions of the language system that allows for those changes, and what pressures on expression drive those changes. Same exact is the familiar case of hyperbole that gave us terribly good and awesome and the British brilliant for “very useful.” And brilliant is itself a dead metaphor.

A twenty-something friend regularly writes “could of and would of” although he had an expensive education and fancies himself a writer, no less. His excuse is, “language is always changing.” But that’s clearly not relevant: he would never write, “I could certainly of, but ofn’t, and you would definitely not of, and in fact you ofn’t.”  So his language hasn’t changed, he’s just chosen to spell the word in one grammatical position as a different word. One response is: what an idiot — can’t he see that his own usage is inconsistent? But the interesting response is: what is it that hides his inconsistency from him? It’s not that he’s incapable of thinking about the use of “have.” Anyone can do that once it’s pointed out. It’s that this “have” is not really a verb at all. That’s where it gets interesting — asking, not judging.

Now what do people think they mean when they say “I could care less”? — especially since “I couldn’t care less” is so incisive and expressive.

fun with Gödel

November 3, 2011

There’s an easy answer to this question, but if you replace c) 60% with 0%, then you get a liar paradox, a Gödel-type statement — it has no numerical answer and can only be evaluated outside its terms.

Gödel, btw, once proved Anselm’s ontological argument, the argument that proves god exists. His version, so far as I can tell, removes all modality in Anselm’s argument, and I think that’s why it works. It’s a complicated version, but I think that even extremely simple, non modal versions work too, e.g., if “god” by definition is that which nothing is greater, then whatever is greatest is that thing. This version works for any model in which there is at least one object. So if nothing exists, then it doesn’t prove anything, but since something patently exists, we can safely assume that there is a greatest thing. (more…)

Dramatizing morality

April 13, 2011

At the start of MIkhalkov’s Burnt by the Sun, the Great Hero of the Stalinist army appears to a platoon of soldiers as himself, barely clothed — he’s just run naked out of his bath, throwing on his pants to save the local peasants from some Stalinist ukase-from-afar. The soldiers don’t recognize him until he grabs a soldier’s army cap and mugs his famous profile for him. It’s the adorable hero as genuine and authentic as well as modest, courageous and good-humored, saving everyone from disaster through his simple honest speech borne of his unalloyed dedication to his country, his people and his army that he believes defends them.

In a moment, the villain of the piece will appear not as himself, but in disguise, lying, playing, charming, insinuating, seducing  — he’s an artist, a musician, a far cry from an honest, simple soldier of simple skills and simple sentiments. He saves nothing and no one. He comes to serve himself regardless of its harm.

Yet who can resist his art? He has them all dancing, like a marionette master. And always dressed, even when swimming, the devlish dandy, even in the bath! His past is riddled with all sorts of whoring jobs, serving any local master, and always playing a double role — a triple role: his local boss, the Stalinist government as an agent, and, of course, himself. No integrity, no authentic public self, no honor, no dignity; all show, all artifice.

This portrayal of villain as brilliant, manipulative artist appealed to me most in this movie. The indictment of the artist is close to my heart. The artist seems to me exactly that: a manipulator, a charlatan, a self-promoter who seduces you to love and adore him, despite your not at all knowing who he really is.

And that is, perhaps, all he is. From the 19th century notion of the artist bringing gifts of the gods, redeeming vile reality, justifying it and comprehending it, here is discovered the vilest motives: seduction, deceit, distraction and distortion. (more…)

Wallace’s solution

April 9, 2011

I’m a little uncomfortable reading Wallace’s book since it was a youthful work not intended for publication, was never published while he lived, and is being published now without his permission. And he left no later comments on it and can’t respond to critics.

Wallace’s solution depends on a scope difference in an alethic tensed modality. Using Taylor’s example: “if the battle occurred, then the admiral must have ordered it” is ambiguous between

1. if the battle occurred, then yesterday it was the case that the admiral must have ordered it

2. if the battle occurred, then it must have been the case that the admiral ordered it

Wallace admits that (1) entails fatalism, but points out that (2) doesn’t. According to (1), the admiral must have ordered the battle, and so had no choice. In (2) the admiral ordered it, but not under duress, as it were, of necessity (must). He had a choice — he might have contemplated several possible worlds in which he orders and several in which he declines to order. It’s just that none of those possible worlds turn out to have been real. That is, yesterday’s world in which the battle was ordered, turns out to have been the only possible world.

But if that’s the only possible world, why is it the only? Wallace seems to show successfully that the answer cannot be the logic alone.

Suppose you are at the moment of ordering. That moment excludes any moment in which you decline to order. That moment includes only moments in which you order the battle. The difference seems to be between whether you have free will or whether you have freedom. Wallace’s draws a nice distinction between fatalism and a kind of post hoc determinism.

Is this a difference without a distinction? If the admiral knows that the moment determines his order (he has no freedom), what does it serve him to have free will? Nothing in the real world. But that accords with our experience: no matter how we plan for the world, the consequences are beyond our ability to control.

The utilitarian/consequentialist effects of determinism and fatalism are equally discouraging. But the entailments for (Kantian)  moral sensibility are completely distinct. Determinism is consistent with holding moral sentiments. Not a fatalist, and that’s why even philosophers spurn it.

On the other hand, while Wallace has found a distinction, I’m not sure that it is telling against Taylor’s view. Relations of necessity among physical effects depend on circumstances, and these are explicit in Taylor’s assumptions. If there is no world in which the order for battle is not given, then the only possible worlds are those in which he chooses to order it. That entails a strange paradox: he is free to choose, but he can only choose one option, not the alternate choice.

How the logic of implication works entirely depends on how you set up the modal system — its axiomata or its inferential rules or both — and its consistency. What makes a system meaningful, assuming it’s consistent, is its usefulness or accuracy. Wallace uses our natural language notions of “it couldn’t have happened” and “it can’t have happened.” That’s good for his system, but not telling against Taylor, since Taylor is specifically using logic against natural language notions which, he is attempting to show, are wrong. And on the other hand,  Wallace’s distinction seems to violate our linguistic, and maybe real-world, understanding of “free.” It may be that the logical syntax should include an inference from

must yesterday order


yesterday must order

or it may be that the inference should be dealt with in the semantics, in the model — in any world in which there is only one option, there is no free choice.

Fear of fatalism

April 8, 2011

Apparently the literature on Taylor’s fatalist argument — the motivation for Wallace’s book (see immediately previous post) — does not include the anepistemic solution I sketched. I’m guessing it’s because everyone is afraid to admit fatalism; everyone wants to believe in free will, and so insists on it. (Believing it and insisting on it are distinct: I insist you have no freedom, but I bet you believe you have. I’ll make a big deal out of that in a moment.)

Having no freedom does not entail making no choices. Freedom ranges over your choices, and your choices depend on your knowledge. If you don’t know the underlying determinations of your choices, those choices will appear to be determined by whatever you do know about. You seem to be making free choices, even though they are not in fact free.

This is not eliminativism, btw. It’s possible to insist that there is no autonomous self and no free will, and still insist that you have a mind and an awareness and your mind contains knowledge of which your mind is aware — or maybe your mind is that awareness of, among other things, that knowledge. Just because I think free will and autonomous self are fictions I am not compelled to give up the mind, knowledge and awareness. Just don’t ask me what awareness is or what role it plays in choice. I’m sure it plays a role, but how, I’m not sure, and having an account is not required for insisting that there is one.

Once you accept determinism, the response to Taylor’s argument is quite simple: the assertion under the modality of real time and its denial in a modality of knowledge don’t contradict. You can know that you are not free and also not know the conditions under which you will choose. So you can insist that no one is free, but still, not knowing the determinations of your choices, you can believe in the fiction of your will. Since you can’t know the sources of your choices, you may believe in any source, including yourself. You can attribute your choices to the devil or the demi-urge or a deity. If you have a sense of personal integrity, you’ll believe that the source is you, because believing in the fiction of you is all you have to be proud of. And those feelings like pride are sui generis. They may be determined by your genetic nature or your cultivated nurture, and you may question them and doubt them, but it’s always you questioning, doubting and feeling. The self has a dual nature: it’s a real melange of sensibilities and thoughts, yet not autonomous. No one has given a good account of it. That’s the appeal of the eliminativists and logical behaviorists and the Wittgensteinian behaviorists. They get on without one.

The formulation in the previous post might be amended to

~K(T) =>


Not only do we not know the future, but we know that we don’t know. That Rumsfeldian modality suffices to absolves us from fatalism. However deterministic the world is, we, with our limited knowledge, know that we can’t know its determinations. That leaves us with our limited knowledge, so regardless of the facts of the future, we are not in a position to assert anything about it with certainty: the contradictory of K~K(T) is not ~T, but ~K~K(T); the contradictory of ~K(T) is K(T), and there is no entailment from ~K(T) in the present to K(T) or ~K(T) in the future — people change their minds or forget from time to time.

Lukasiewicz, bivalence and the future

April 7, 2011

Just now looking at David Foster Wallace’s Fate, Time and Language, I’m puzzled by Lukasiewicz’ argument, quoted in his text, that statements about the future cannot be true or false at the moment when they are stated. It seems obvious to me that any statement about the future must be true or false, it’s just that we don’t know their truth value at the moment (except for necessary truths and inconsistent statements which may be deemed false and if contradictory, plainly false).
~K(p) does not imply (p) or (~p).
Not knowing the truth value of a statement means that the epistemic certainty of it has a degree of probability <1. But that doesn’t imply that the proposition itself has a certainty <1. The proposition itself has a probability of either 1 or 0. Why would anyone conflate the epistemic with the realis assertive?

Am I missing something? The probability of a belief for a determinist depends on the known circumstances. Those known circumstances often do not suffice for certainty.

The issue for Lukaseiwicz lies in the way we speak about possibility. If I say, “I will be at your place tonight,” even I can’t say for sure that I really will get there — I could get run over, I could get distracted by a friend. So we venture to say that it’s possible I’ll get there, and, likewise, it’s possible that I won’t. Using P for “possible” and T for “I’ll get there tonight”

P(T) & P~(T)

When the future arrives, we’ll know which of the conjuncts is true. If we’re not determinists, there’s no problem. But if we’re determinists, then one of these conjuncts is necessarily true, and the other necessarily false: necessity is interchangeable with “not possibly not,” and “necessarily not” is interchangeable with “not possibly”:

N(T) = ~P~(T)

N~(T) = ~P(T)

but if T is true, then the statement before the future arrived, added to our knowledge of necessity now in the future, yields a contradiction

N(T) & P~(T) =

~P~(T) & P~(T) =

N(T) & ~N(T)

and if T turns out to be false

N~(T) & P(T) =

N~(T) & ~N~(T) =

~P(T) & P(T)

Now, if we are not determinists, there’s no problem: the future isn’t necessary, so the truth value at the future doesn’t contradict any assertion in the past. So non determinists can assert that propositions about the future have distinct possibilities. But if we buy into determinism, we can’t assign probabilities to propositions about the future. So Lukawiewicz offered to abandon bivalence: statements about the future are neither true nor false, but somewhere in between.

But all that’s ignoring the epistemic context of our assertions of possibility. The correct formulation of our assertions, if we are determinists-in-ignorance is:

B(P(T) & P~(T))

“I believe that possibly T and possibly not T” or alternatively

B(P(T)) & B(P~(T))

“I believe possibly T and I believe possibly not T”

Believing possibly T or possibly not T is in no way inconsistent with T or ~T or N(T) or N~(T).

B(P(T) & P~(T)) & N(T)

is consistent, as is

B(P(T) & P~(T)) & N~(T)

A simpler formulation uses the anepistemic mode


“I don’t know T for sure” which itself implies


“I don’t know ~T for sure” and therefore

~K(T) & ~K(~T)

(I’m leaving out for the moment the possibility that ~K(T) can mean “I don’t know of T,” which allows for three possibilities: I don’t know that T is true, I don’t know that T is false, I don’t know of T at all)

These are also consistent with either of T or ~T or their modal necessary versions. There are no contradictions here:

~K(T) & ~K(~T) & N(T)

~K(T) & ~K(~T) & N~(T)

The implication is that “I might not be there tonight” means both that I don’t know whether I’ll be there or not — it means the exact same as “I might be there tonight.”
Elsewhere I’ve given the evidence of the equivalence:
???I might go but I will
???I might go and I will
???I might go but I won’t
???I might go and I won’t
???I might not go but I will
???I might not go and I will
???I might not go but I won’t
???I might not go and I won’t
Unless the speaker has had a change of mind mid-utterance, these sentences are semantically incoherent. It is uncontroversial that the consequent conjuncts assert certainty over intention, so, presumably the incoherence lies in the uncertainty of the antecedent conjunct. Since the same certainties clash with the negation or without, the implication is that “might” and “might not” bear the same uncertainty: “I might not go” implies “I might go” and both can be cashed out as the anepistemic



~K(G) & ~K(~G)

but not  ~K(G & ~G) unless we’re very contrary, since we all know


and we know that we know it, too.