Archive for the ‘semantic’ Category

Liar paradoxes, a problem with reductio proof and speech acts

June 20, 2013

It’s easy to mistake paradoxical sentences for liar paradoxes. “If this sentence is true, then it is false,” is a liar paradox. If the sentence is true, then the antecedent is true. If the antecedent is true, then the consequent must be false, the implication as a whole is false, so the sentence must be false. So if the sentence is true, then it is a contradiction and a falsehood. So the antecedent must not be true. If the sentence is false, antecedent is false, and the implication as a whole is true.

“If this sentence is false, then it is true,” however, is not a liar paradox. If it is false, then the antecedent is true and the implication fails, and the whole is false. If the sentence is true, then the antecedent is false, the implication holds, and the sentence is true. That’s not a paradox, it’s just a sentence the truth of which cannot be determined. It’s like the sentence, “This sentence is true.” Is it true or false? How could you tell?

Similarly, “The sentence I am now writing is true,” is indeterminate. “The sentence I am now writing is false” is provably a liar paradox, athough one could ask of these two sentences “true or false of what?” The deductive proof that yields a liar paradox of the latter, is a reductio: assume the sentence is true, you deduce that it is false; assume it’s false, you deduce it’s true. So if it’s true, it’s false and vice versa. But if you ask “true of what?” then you’re asking for an empirical answer — does the sentence corresponds to something, in this case to its own truth. Is truth a thing that can be pointed to? If it’s a correspondence with something, we’re stuck in an infinite recursion. So these sentences, on the one hand, lead to a questioning of the correspondence theory. But they also lead to questioning of the validity of deductive reductio argumentation, not unlike that questioning of the reductios that led Cantor to multiple levels of infinities, and the intuitionist rejection of the reductio in favor of proof by demonstration. Several directions from here: you can say these sentences don’t correspond to anything; or correspondence is not complete; or correspondence, even with its incompleteness is a better option than reductios that lead to liar paradoxes.  (more…)

possible or not

May 10, 2012

Is it possible to swim the Atlantic?
An ex neighbor points out that if “possibly” doesn’t imply also “possibly not” then how is “possibly” different from necessity? Doesn’t “Life on Mars is possible” mean “It’s also possible that there’s no life on Mars”? And doesn’t it also mean “Life on Mars isn’t necessary”?
Grice gave an answer to this question, and I’ve written about it elsewhere in this blog, but I think there’s more to be said and I want to try to sort all of them out.
Suppose Goldbach’s postulate is possibly true. Suppose someone proves it. Now it’s necessarily true. Is it no longer possibly true?
My neighbor says no. I think Lukasciewicz agreed with him. (more…)

Aymara, trivalence, competing satisfaction and modality

January 6, 2012

In his monograph on the trivalent logic of Aymara, Ivan Guzman de Rojas sets out to show that a trivalent logic can reach conclusions unavailable to bivalent logic. I want to tease out the import and accuracy of this extraordinary claim, and try to understand its significance for modal logic.

Consider two circumstances: p) there’s smoke; q) there’s fire.



January 4, 2012

I see that Wikipedia’s article on ternary logic references Aymara “a Bolivian language famous for using ternary rather than binary logic.” Aside from the vaunted adjective “famous,” I am skeptical of the claim that Aymara uses a ternary logic rather than binary, skeptical also of the presupposition that natural languages use a particular logic rather than another logic, and skeptical as well of the implicature that other languages use only binary logic, infamously or otherwise.

Much of the excitement over Aymara derives from a monograph written  in the 1980’s by an engineer and machine translation pioneer, Ivan Guzman de Rojas, who observed that Aymara indicated in its inflections the degree of certitude of its respective assertions. He takes these as logical operators, just as “not” can be taken in English as a negation operator: in English, “not” takes a true statement into a false one, and a false one into a true one. E.g.,

snow is white =>True;  snow is not white =>False

snow is green =>False; snow is not green =>True

Aymara, however, also uses an inflection that takes a true statement into a neither-true-nor-false statement. This shows, he claims, that Aymara uses a third truth value, neither-true-nor-false, which is used for uncertainty.

He says, further, that the ternary logic allows the Aymara people to derive logical conclusions that are not available in binary logic, and that the Aymara people think differently from people who are limited to binary logic.

It may already have occurred to the reader that English does have exactly such an operator, “might”:

snow will fall;  snow will not fall; snow might fall

that is, “might” takes an assertion or its negation into an uncertainty.

Does this mean that English has a third truth value? Well, yes and no. (more…)

mixing speech and non contextual logic

October 29, 2011

Geach and Horwich both criticise Strawson’s performative analysis of the truth predicate in English on grounds that seem to me not only mistaken, but a common mistake, really a category error, conflating the speech situation with logic uncontextualized — the logic you study in college. Not just a common mistake, it’s just about everywhere. Here’s their argument:

If Strawson is right that the truth predicate is some kind of gesture of agreement, then accepted deductive arguments will fail, e.g.,

1. Phil’s claim is true

2. Phil’s claim is that snow is white

3. conclusion: snow is white.

If (1) means that the speaker is agreeing with Phil’s claim, then there’s no deduction from the speaker’s agreement to the fact in the conlcusion. At best, the argument concludes that the speaker agrees that snow is white. But even that wouldn’t hold, since agreement, like belief, is probably an opaque context — imagine a speaker who always agrees with Phil whether he knows the details of what Phil thinks, not knowing that Phil has been deceived by someone and believes something that the speaker knows is false.

The Horwich argument is itself a fallacy of equivocation. Assertions in logic are distinct from logical assertions in speech. Speech is always contextualized, so no facts about the world can ever be deduced from it, except the facts of the speakings and believings and, following Strawson, the gestures indicating attitude. To get from speech to facts, you have to move on up to a meta-assertion like, <If S said x and x is true, then what S says is in fact true of the world> where the words “and x is true” is not spoken by any speaker, but sits in a noncontextual world of assertions about the world.

The proper form of the argument in speech goes like this:

1. (I assert/believe) Phil’s claim is true = (I assert/believe) I agree with Phil’s claim

2. Phil’s claim = snow is white

3. (I assert/believe) snow is white is true = (I assert/believe) I agree that snow is white

Now (1) is still an opaque context, so the conclusion might actually not fit with the speaker’s actual prima facie beliefs, but this is exactly the right argument to show why the context is opaque. It’s armed with this argument that you confront the speaker who doesn’t believe that snow is white but who does believe whatever Phil claims, and explain that there’s something wrong with his assumptions about Phil’s claims. That is to say, this argument shouldn’t arrive at any better conclusion than the one it does.

There is, I think, vast confusion about this. You simply can’t shift from speech to non contextual logic. One is necessarily opaque, the other transparent. To derive facts from speech beyond the facts of the speech and it’s speaker, you need a metalanguage.

Now, you might ask whether there is such a thing as non contextual logic — aren’t all statements spoken or written by some speaker or writer. The answer is, that’s solipsism and should be assumed and forgiven. Alternatively, add a hypothetical meta-metalanguage beyond the solipsistic language. It’ll be speculative — “suppose there is a noncontextual logic and it says…”.

A theory for semantic drift

April 1, 2011

Okay, here’s a theory to account for some of the variety in semantic drift, the gradual change of a word’s meaning.

Going back to old Saussure, the sign has two sides, the physical shape (for speech, this is the sound of the word) and what the word means. You’d think that semantic shift would only happen on the meaning side, but semantics plays on both sides of the sign because both sides relate to other signs in the language.

Let’s expand Saussure’s duality a bit with Frege’s distinction between sense (something like idea) and reference (the real world objects determined by the idea). The meaning of the sign can shift if the idea drifts, expanding (losing information) or contracting (becoming informationally richer) or just replacing some information with new information. The many pressures or inclinations on idea drift have been well observed and studied in the literature.

The physical sound-shape side of the sign can be the source of meaning shift as well, odd as that may seem. Why would an arbitrary sound have an effect on meaning? Well, for example, sound shapes in English that bear strong resemblance to Greek or Latin words tend to be treated as more serious and formal than monosyllabic Anglo-Saxon words. That seriousness affects their semantic value. Ask a class of students which endeavor is more fun and which more serious, athletics or sports, and you will get a 90% agreement that sports are a less formal activity, although if you then ask whether they denote the same set of activities, you’ll get 100% agreement that they do (and a puzzled class of students).

Speakers have a blind spot in their linguistic capacity. They have great trouble distinguishing between the word and its meaning. There’s nothing surprising about it: we do a lot of our thinking in words, so the two — thought and word — incline to meld into one another.

So it is also not surprising that the formality of a word can influence its semantic shifts. Our social attitude to a word’s sound-place in the language is part of its meaning.

So far we’ve got the following aspects of meaning:

– idea

– social attitude to the idea and relation of the idea to other ideas

– attitude to the sound shape and the relation of the sound shape to other sound shapes

– reference.

Less observed is the possibility of drift caused by the reference.

The set of real-world objects referred to by a word is determined by the idea. The idea of the word “cat” determines the set of felines. When the idea is employed colloquially as in “hep cat,” the idea determines that “cat” denotes the set of counterculturally acceptable males. Because the referent depends on the idea, drift in the idea has received most scientific attention. But the referent, even though fixed by the idea, can be the source of semantic shift as well, because social attitudes to things is not fixed.
“Democracy” denotes a specific set of government types, but that set has not always been valued in the past as it is today. In the U.S., “democracy” is viewed as almost synonymous with “just” and “right.” It wasn’t always and it need not always be.

Consider the denotation of “woman.” The boundaries of the set haven’t changed, and the properties that make a human a woman haven’t changed, but social attitudes have and the social place of women has. Surely these changes, which relate to the referent, not to the idea or the sound shape, have shifted the meaning.

“God” is another word that has surely shifted through changing attitudes to its referent, though discussing it presents the difficulty of dealing with an elusive referent.

Consider “computer.” The rapid technological advances have altered the set almost beyond recognition, from a room-sized machine exclusive to universities and military labs, to the palm pilot. That’s a reference change that directly shifts the idea.

One reason linguists don’t spend much effort observing reference-based shifts, is that those shifts depend on non linguistic phenomena, and so don’t instruct much about the nature of language itself. It would be useful, however, to learn the extent to which reference shift can be tolerated by a word and the broader linguistic effects of reference shift.

Then there’s metaphor. In a separate post I mentioned that metaphors trade on a few specifics of an analogy. They can dilute information as in

– the foot of the mountain

now means just the bottom — the toes, heel and arch are lost.

This is all just a start, but the point here is that semantic shift can occur on either side of the sign, the reference or the idea, the signified or the signifier.

I’m going to stop here for now, but there’s more in the first post on this blog, which gives a bunch of surprising facts and more surprising dynamics about semantic drift in gender words. The big surprise there is that euphemism frequently causes its opposite, pejoration.

Saving Grice’s theory of ‘and’ (with Kratzer lumps!)

June 11, 2007

I’ve always considered Grice’s theory of conversational implicature to be one of the most beautiful theories around. But nowhere is beauty so tightly yoked to truth as in the sciences, where beauty, in the form of simplicity, will decide the truth of two otherwise equally powerful theories. (It’s kind of remarkable when you think about it — truth and simplicity seem not only distinct, but unrelated, unlike say, truth and accuracy or consistency. A complex theory will cause more complexity in its relation to other theories, but if it’s still true, why should complexity ever matter? Is preference for simplicity just a bias?) Truth seems to be a necessary condition for the beauty of a theory in science, so if Grice’s theory isn’t true, its beauty all is lost. The application of conversational co-operation gets messy at and, impugning its truth. I’ve got an idea on how to clean up the mess and restore the symmetry of the structure.

Grice’s analysis of “and” goes like this:

Sometimes “and” is interpreted as simple logical conjunction

1. I brought cheese and bread and wine.

The order of conjuncts doesn’t change the meaning: I brought bread and cheese and wine; wine and cheese and bread; bread and wine and cheese; wine and bread and cheese; it’s all the same. This use of and is symmetric, exactly like the logical conjunction &: A&B<=>B&A

But sometimes and carries the sense of temporal order, “and then”

2. I took off my boots and climbed into bed.

(I think I got this example from Ed Bendix some years ago)

This conjunction is not symmetric: taking off your boots and then climbing into bed is not the same as climbing into bed and then taking off your boots, and the proof of the difference, you might say, comes out in the wash.

The difference in meaning, according to Grice, arises from the assumption that the speaker would not withhold relevant information or present it in a confusing form. If the order of events matters, the order of presentation will follow the order events, unless otherwise specifically indicated. So if I said

I climbed into bed and took off my boots

you’d be justified in surmising that I’d come home very late and very drunk.

The theory of conversational implicature avoids the undesirable circumstance that there might actually be two homonymic “and”s in English, one meaning “&” and the other meaning “and then.”

A problem for Grice was observed long ago by Bar-Lev and Palacas (1980, “Semantic command over pragmatic priority,” Lingua 51). They noted this wonderful minimal pair:

3. I stayed home. I got sick.
4. I stayed home and got sick.

If Grice is right, (3) should mean

3′. I stayed home and then got sick.

But it doesn’t. It means

3″. I got sick and therefore stayed home.

Now unless we are willing to say that the sentential boundary is a morpheme with meaning, we are compelled to drop Grice. Worse still, even though (3) means (3″), the sense of “and then” returns immediately we add “and” between the sentences. (4) means

4″. I stayed home and then I got sick.

even though that’s semantically unexpected. So it’s not about semantic bias, this violation of Grice’s principle. It’s a very real problem that Bar-Lev and Palacas pointed out.

So what’s with “and”?

Here’s my suggestion.

a. In order to use “and” you’ve got to be introducing something new. Think of Angelika Kratzer’s lumps of thought: you’d never say “I painted a portrait and my sister” if you’d only painted one portrait and it was of your sister. Information is structured in clumps of truths that the logical connectives don’t respect. Yes, a portrait was painted and a sister was painted, but if these two things were accomplished in the same act of painting a portrait of one’s sister, then they are in some sense the same fact, though two truths. Now notice the difference between :

“I painted a portrait. I painted my sister.”

Could be the same event. Not so easy to get the same-event interpretation from

“I painted a portrait and I painted my sister.”

The and implies a distinct, newly introduced fact not lumpable with the antecedent event.

b. Causal relations are internal to an event.

Put (a) and (b) together and you have an explanation for (3) and (4). I have a good deal more to say about this, but it’s really nice out, and I’ve been in all day. (more…)

Euphemism and euideism: distinct semantic strategies for French and Latin borrowed words

June 11, 2007

The replacement of one idea for another is a strategy that looks like euphemism but is distinct from it. I’d like to call it euideism: just as euphemisms are acceptable word forms for taboo word forms, euideisms replace taboo ideas with acceptable ones. The difference between these two strategies plays upon the twofold nature of the sign observed so long ago by old Saussure: sound shape (word form) and referent (idea) —

euphemism is motivated by an attempt to replace one sound shape for another

euideism is motivated by an attempt to replace one referent for another.

The distinction also plays into differences in register between Anglo-Saxon, French-derived and Latin/Greek-derived vocabulary in English. (more…)

Ladies and lords: refitting the feminist model of pejoration

June 11, 2007

It’s become a chestnut of feminist linguistics — maybe it’s better to call it gender linguistics, to remove the politics from the science, if that’s possible or wise — that the frequent pejoration of words for disempowered people on the one hand, and the frequent pejoration of words denoting women on the other, strongly implies that women have been socially disempowered through the history of the language (as if one needed evidence for this!). Words like “knave,” which once meant simply ‘boy,’ and “villein” which meant merely ‘peasant’ have pejorated, and even “boy” is pejorating in exactly the way “knave” did: “I’ll get my boys on it” says the pop culture mobster, meaning not that he’ll get his male children to do it, but that he’ll get his servants, his henchmen. On the other hand, words denoting objects of value don’t pejorate even if they are female: the generic term for cattle is “cow,” for Daffy’s cousins, “duck” not “drake.”

I’m not going to contest the disempowerment of women, but I think the feminist correlation is too neat. The dynamics of pejoration seem to differ depending on the word, some showing signs of disempowerment, some not, so it is good to look at the cases one by one. I have in mind the female&male pairs

lady, lord

governess, governor

queen, king

madam, sir

princess, prince

all of which niftily show pejoration in the female-, not in the male-denoting word.


Starting with “lady,” the pejoration of which does, I think, show a gender difference in empowerment or prestige: the word began as a designation for the wife of the Anglo-Saxon chief. Each tribe cultivated its warriors, bringing them all under one roof of the chief’s house (remember King Lear and his rowdy entourage his daughters refused to host — Lear was an Anglo-Saxon king). In the warriors’ big house, the chief was the warden of the loaves, or “hlafweard,” (later “laward,” eventually “lord”) and she the loaf kneeder, the “hlafdige” (later “lavedi,” eventually “lady”). A difference in power and prestige is obvious at the origin. Even though labor is more essential to social survival, it is distinguished here from authority and possession which are handed to the male of the pair.

But “lady” was not without prestige. Most important, she and the lord were socially unique. There was but one lady per tribe. The closest equivalent in present-day English would be “queen.” Subordinate she may have been, but she received her tribe’s deference deflected from her husband.

Power relations changed under the Normans. The unique Anglo-Saxon chieftain was replaced with a class of superiors. Under occupation, all the occupiers may as well be kings with respect to the occupied. And the words “lord” and “lady” reflect this widening of denotation, but “lady” much more than “lord.” Feudal Norman male-oriented culture may have helped sustain the prestige and uniqueness of “lord” and while there were many Norman lords and ladies, there was still only one ruling lord in the land, but no corresponding ruling lady.

Dick Leith, in his Social History of English, tells a story of the replacement of informal “thou” with formal”you” in class-mobile industrial society where one never knows who is a genuine social superior and who is just new money, so people hedge their bets to err on the side of formality just in case. No doubt the same with “lady.” And again, the association of unique power to rule may have prevented “lord” from wallowing in such commonality. To have many ladies in ones social order may be an embarrassment of riches, but it is no contradiction. To have many lords is both. And so, today a lady is distinguished from the general class of adult females by the least mark of prestige. That it retains some prestige is evident from its ironic use in “ladies of the night,” which wouldn’t hold its humor and irony if it weren’t that whores don’t count in the usual inventory of the set denoted by “lady.”

The word today is full of surprising contrasts. As a common title of address it is formal but insulting:
Excuse me, lady (so demeaning it isn’t used anymore)
Excuse me, miss (according to my students, always preferred to “ma’am”)
As a descriptor, it is distinguishable from “woman” only in its absence of sexual, warm-blooded connotation
It’s that lady over there
It’s that woman over there

Sensitivity to gender inequality is rendering this “lady” obsolete. It survives in “ladies and gentleman,” and in circumstances where “gentlemen” is perceived as too formal, “women” is often perceived as too human.
The men on the left, ladies to the right
though it can depend on the gender of the speaker — women in polite situations often seem to feel the need to show more delicacy addressing men and vice versa.

The standard denotation of “lady” has widened immensely, spreading its girth almost to cover the entire class of adult females, its only vestige of prestige its lack of human warmth and sexuality.

However, it has great vitality as a colloquialism, where its connotations of dignity and respect reappear. Your lady is your girlfriend. It’s a title that seems to combine endearment with deflected respect (my woman deserves the respect I demand for myself) and subordination all rolled into one. Not too far from “hlafedige.”


As a term of address and a title, this word has not lost any more prestige than its male counterpart. The expansion of both reflects the decline from feudal rules to bourgeois pleasantries. It’s its use as a euphemism for the brothel administratrix that is claimed by feminists to distinguish “madam” from “sir.” It must be the power of the prestigious male that spares “sir” the place of “pimp.”

I don’t think so. Euphemism replaces an unacceptable word or covers an unacceptable idea with an acceptable word. (There are euideisms as well, but I leave that for another discussion.) There’s no eu if the stand-in word isn’t in itself acceptable and prestigious. In the case of “madam,” the denotation itself commands some respect. The pop culture image of the madam is full of dignity. She resembles nothing so much as an imperious, rigid, protective prioress of an abbey, and she’s usually tougher to bring down. The image of the pimp: a vile and villainous, cheaply and comically pretentious, tasteless and reprehensible predator. The pimp holds a special place in our culture. He is universally despised. There have been many sympathetic treatments of drug addicts, whores, indigents and criminals of all sorts, murderers, rapists, serial killers, even Hitler is probed for his motives and the possibility of an underlying human interest, but the pimp is such an unworthy worm no one will take his cause even to investigate his human motives. Why euphemize him? We don’t.

(A pander is a different person entirely.)

Euphemism as a road to pejoration doesn’t always prove disempowerment. But it does by definition prove the prestige of the euphemic word. If the euphemic word doesn’t have some prestige, then it can’t serve as a euphemism, there is no euphemism. Euphemisms have prestige by definition.


Another case of euphemism. And again, it is the prestige of the word and the (small) prestige of the position that invites the euphemy. And it’s not just a euphemism for baby-sitter or nanny: it pays better and provides better references and maybe even accommodations of an au pair. Apparently “governor” has undergone worse as “gov’nah” though not stateside, where governors all rule one or another of the fifty states of the union. Other uses of “governor” have an air of anachronism in the US.

The point here is not to deny that the female-denoting word has pejorated — it has — but to learn something from the particular process of pejoration. It is not enough to describe these euphemisms as simple reflections of lack of empowerment or prestige. Euphemism is a reflection of prestige, not its lack. The euphemism is dragged down by the denotation of the word it replaces, not by social disempowerment. It’s a case of no good deed going unpunished. The feminist story is not entirely wrong. It’s just partial.


Gender inequality is most evident here at the top. There’s no “queen of the mountain,” no female Elvis “the Queen,” no “Queen Kong.” The cross-gender epithet carries such an intensely negative implication, that one has to wonder whether males have commandeered social affect and mores in the language, here at least. Male disparagement of femininity is nowhere more evident than in this one epithet that equates everything anathema to manhood with womanhood, and not just womanhood, but the ultimate woman, the queen. The word virtue itself derives from Latin vir, ‘man.’ We’re at a puzzling place for the understanding of linguistic values. Mothers’ linguistic influence is surely greater on children, male or female, than fathers’. So what is the origin of this capitulation to maleness? Were women so thoroughly marginalized in common discourse? Were they treated as mere chattel? Judging from the language, they were.

More later, I have to get to rehearsal.