It’s interesting to think how fundamentally impossible it is to parse a sentence without a background corpus of knowledge about the world:
> I dropped the hammer on the table and it smashed
> I dropped the vase on the table and it smashed
Exact same grammatical structure but if you switch the noun the way you parse the sentence changes. This is why machine learning with huge datasets wins in NLP, translation etc.
Samuel Delany thought this was part of science fiction too [0]:
> There's often a literal side to SF language. There are many strings of words that can appear both in an SF text and in an ordinary text of naturalistic fiction. But when they appear in a naturalistic text we interpret them one way, and when they appear in an SF text we interpret them another. Let me illustrate this by some examples I've used many times before. The phrase "her world exploded" in a naturalistic text will be a metaphor for a female character's emotional state; but in an SF text, if you had the same words— "her world exploded"—you'd have to maintain the possibility that they meant: a planet belonging to a woman blew up. Similarly the phrase, "he turned on his left side." In a naturalistic text, it would most probably refer to a man's insomniac tossings. But in an SF text the phrase might easily mean a male reached down and flipped the switch activating his sinestral flank. Or even that he attacked his left side. Often what happens with specifically S F language is that the most literal meaning is valorized.
I recently learned that a number of African cultures used "memory devices" in order to assist in the recall of oral histories. Essentially, positions of beads on an intricately-carved board indicated to the practitioner what to speak next, out of a massive corpus of knowledge. Looking at the amount of background knowledge necessary to make Eurasian written documents intelligible, though, I begin to wonder if the common notion that SoS Africa had no written language before colonialism is inaccurate. In both cases, you have esoteric data recording methodologies that can't be deciphered without essentially already knowing what's being communicated, albeit not structured as presented. Makes you wonder how many other ways of recording history that we, raised in a Eurasian tradition of transcribed alphabets/syllabaries encoding lexical thought, completely overlook because we simply have no concept of recording and conveying thoughts another way.
When I was in undergrad I was helping out a PhD student in computer science, working on how to parse English. One of his test cases was, "I saw the man on the hill with a telescope." for which there is of course no one possible meaning.
I was told years later the company he worked for at the time (this was the mid 1980's) was the CIA (and to my memory, he only ever told me "his company" and never named it while we were working together). I don't know if or how any of my "help" made it into the US gov't, but I think about it sometimes.
Interesting, but I think that it's unlikely someone would say that an ordinary wooden pencil was smashed, short of some more catastrophic action. A pencil might have broken, but not smashed.
"We fired the pencil at a brick wall and it smashed" ... okay, it's probably the pencil that smashed.
Perhaps a mechanical pencil, but again, that seems odd and unlikely.
All of this requires a whole lot of knowledge about the world:
- Pencils are generally made from wood, wood is a material that's more likely to deform or break rather than shatter
- Tables can have tops that are made from materials that are more likely to shatter than deform/absorb the shock.
My first intuition is that ‘it’ refers to an unmentioned object, one so fragile that it can be smashed by a falling pencil. Some kind of toothpick architectural model maybe?
Not necessarily, in this case I didn't reject the phrase "I dropped the pencil on the table and it smashed." as semantically implausible because of its context (it was used close to similar-looking phrases). Of course that it doesn't inform us anything about any "pencil" nor "table", but it does inform us about the limits (or non-limits) of AI.
In that context smashed probably takes on a different meaning as a sound, and the sentence semantics are equivalent to "the pen clattered loudly on the table". Similar to how the word would work if someone talked about "the smash of cymbals". It would be an awkward sentence though.
One of the most influential philosophical concepts for me from the last decade was from this very blog called “Nebulosity”. It just speaks to the nature of reality that is misinterpreted with overlays of meaning.
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‘Nebulosity’ refers to the insubstantial, amorphous, non-separable, transient, ambiguous nature of meaningness.
From a distance, clouds can look solid; close-up they are mere fog, which can even be so thin it becomes invisible when you enter it.
Clouds often have vague boundaries and no particular shape.
It can be impossible to say where one cloud ends and another begins; whether two bits of cloud are connected or not; or to count the number of clouds in a section of the sky.
If you watch a cloud for a few minutes, it may change shape and size, or evaporate into nothing. But it is impossible to find an exact moment at which it ceases to exist.
It can be impossible to say even whether there is a cloud in a particular place, or not.
Maybe I'm missing a subtlety of your meaning here (how appropriate) but I know that philosophers have discussed such things for centuries; e.g. 2 grains of sand is not a pile, 1000 grains is, but where is the transition?
Fuzzy logic in the broad sense (not necessarily the logic of the Zadeh operators, for instance) seems to provide the best answer: there is no crisp transition; membership is real-valued, not binary.
So much effort wasted based on trying to derive fundamental meaning from coincident attributes of our brains' neurological implementation of abstract concepts.
"The transition is wherever your 'pile' classifier neuron fires."
I think you are selling at least some of the philosophers short. What is a pile and isn't a pile is not entirely subjective (i.e. we all agree that 1 grain of sand is not a pile), nor is it entirely objective (in the sense that different people will probably draw the line at different places). On top of that, the transition even for a single individual is not abrupt.
Understanding and dissecting these sorts of ambiguities with something as inoffensive as piles of sand can be useful for better understanding disagreement that stems from ambiguity when things are more contentious.
Yeah but those properties are exactly what you would expect from imitation learned fuzzy neuronal classifiers. As such, they have no deeper meaning than saying "does the fact that the deep learning model thinks this traffic cone is a penguin reveal to us a deep truth about traffic cones and penguins?" No.. It just used some shortcut feature that's not universally applicable. Just like us.
The heap classifier works to tell that obvious heaps are heaps. It works to tell that single items are not heaps. In between, there is no meaning but noise.
I think that's a little too reductionist – in that I'm not sure that there is one neuron responsible for pile classification in that way. But as a metaphor, it's a very good sentiment.
Most of it isn't new, but David Chapman is better at explaining nebulosity and putting it into perspective than anyone I know, so I recommend reading more of his stuff.
English is a language with pretty reduced inflection mechanisms and overloaded word meanings. Translated into Russian you would be forced to use different builds for different meanings: “St. trinian’s is a pretty (in female gender, nominative case) school for little (in female gender, genitive case) girls” or “St. Trinian’s is a school for pretty little (both female gender, genitive case) girls”.
It's true that languages with case declensions (beyond the vestigial declined pronoun forms in English) would be less ambiguous in expressing that example sentence.
English is an analytic language, meaning that more information is conveyed through syntactic patterning involving closed classes of words like particles, prepositions, and articles. These words could be considered "overloaded" as you said, but for non-closed classes of words though, as far as I know English is not known to be more or less polysemic than other languages.
but seriously, in contrast to natural language, the article lays out the basics of mathematically-based logic, not for its own accord, but as groundwork for the more interesting later sections talking about context-dependence and reasonableness.
the reason natural language has so much ambiguity is not because our brains couldn't have come up with a rigorously logical language, but because the world is ambiguous and language reflects that.
Also time constraints. It's possible to be much more precise even with informal language, but it would take forever.
So, for efficiency, words don't really deliver an idea to the listener. Instead, it's assumed that the listener is working toward the idea through their own reasoning, and words fill in only the necessary gaps to help them get there or to help them get there more quickly.
You more or less reverse engineer what their thought process must be, then you do a gap analysis between what they're probably thinking and what you want them to be thinking, and you give them the pieces of info necessary for them to make the leap.
Poul Anderson in "Brain Wave" had a most interesting take on what increased intelligence would look like. People said less and less to each other, but conveyed more meaning.
>but because the world is ambiguous and language reflects that.
This doesn't seem like a very satisfying explanation. Take one particular example of a structurally ambiguous sentence of English:
"The company couldn't make the car fast enough".
The two meanings are completely distinct (speed of production vs. speed of the car). There's no fuzziness about this distinction out there in the world. The speed at which a car travels and the speed at which it's made are two completely distinct properties.
That is an interesting example because it looks like semantic ambiguity rather than syntactic ambiguity. But actually it is about structure as you commented -- something like this:
Regarding the meat of your comment, it is quite difficult to banish all ambiguity from natural language for a variety of reasons, but we don't really need to: humans are incredibly good at handling linguistic ambiguity. There has been a lot of fascinating research on the topic: in particular, I recommend reading up about anaphora resolution[0] and garden path sentence repair[1], because the literature includes some info on what is happening in the brain, which is significantly more detailed than what exists for most other types of linguistic ambiguity.
All of this ambiguity in natural language is something that continues to be huge hurdle for NLP: it turns out that fetching the right information from the context to resolve all the ambiguities that arise in a single conversation is completely non-trivial, despite how easy humans make it look!
An interesting case study in the opposite direction (ie attempting to remove ambiguities from natural language) is Ithkuil[2]: it is a conlang that attempted to completely banish (semantic and lexical) ambiguity and it ended up being ridiculously hard to use or learn at all.
If anyone is curious, you can plug those trees into here (http://mshang.ca/syntree/) and it will draw them for you. But my tree drawing skills are very rusty, so they are pretty basic/bad.
I'm confused about your sentence parse notation. Isn't "fast" an adjective in one of the interpretations (namely the one parsed the same as "The company couldn't make the car safe enough")?
Doesn't that "safe" example point out something else? The example with "fast" is only ambiguous because it's common to use "fast" as both an adjective and an adverb? The sentence with "safe" doesn't sound to me like an acceptable way to say that the company's manufacturing process was too dangerous.
For the alternative meaning, I think you'd say, "The company couldn't make the car safely enough." So yeah, adjective and adverb, I think you're right. For that matter, "The company couldn't make the car quickly enough" would resolve the ambiguity in one direction, but I guess not the other.
It's true that there might also be a lexical ambiguity here, but the two interpretations do also correspond to different syntactic structures. The adjectival phrase attaches to an NP whereas the adverbial phrase attaches to the VP (or thereabouts).
And yet, in the real world, people could use that sentence as part of a discussion without causing any confusion or ambiguity. Because sentences don’t exist on their own, they have a wider context which can focus their meaning.
Human language is succinct. We don’t generally say twenty words when ten would do. If the context made your example sentence clear, why would a speaker need to add any words to clarify it further?
For the record: Clinton was making a banal and uncontroversial, if inartfully stated (and awfully hilarious in hindsight), observation on the tense of a verb. He was right, actually. But yeah, that was a sound bite for the ages.
One other factor is that our brains _are_ able to do it. I guess we merge the sentence with our context and gradually realize the meaning, while rejecting the more bizarre parses without thinking twice about them. On the other hand, it is quite possible to stump humans with out-of-context questions and statements. In these moments we realize how much we rely on context.
I would say it is more than the world, we use language to discuss our intentions, desires, beliefs, willingness, etc. All of which there is value to speakers to being ambiguous. Some languages are even better than English at giving speakers the ability to dial up or down ambiguity when expressing ostensibly the same intention, in ways that a careful listener would find signal in.
Frege did not in general reject intuition. The rules of what became first-order logic are accepted on the grounds that they are intuitively undeniable and provide the results we need. That's the actual lesson of Russel's paradox in response to Basic Law V: that blatantly obvious things can be problematic.
For anyone interested in the semantic analysis of the verb "to be", I recommend Andrea Moro's book "A Brief History of the Verb To Be."
Also note that analytic philosophy is the philosophical tradition the author is referring to, not rationalism [2]. This is an ahistorical use of the latter word. They did define their terms in the glossary but that won't help you in searching.
I think it's a poor example, because whether or not an eggplant is considered a fruit depends on your perspective and context. It is a fruit botanically, but it is not typically considered or used as one for culinary purposes.
That distinction of ambiguity adds an interesting complexity to "meaningness," but I agree that it's confusing in relationship to the rest of this specific article.
Alright, that was the only thing I could thing of that would cause my confusion here. I viewed it simply as 'it's False to say all eggplants are fruits' but I guess the author's intention was 'because people consider eggplants to be culinarily a vegetable, saying all eggplants are fruits is False'.
It's an interesting addition to the disgusting about meaning in linguistics, but according to formal logic as used by linguistics, is the eggplant example even correct? It seems as though no matter what, 'an eggplant is a fruit' is True, and perhaps there is a different logical notation to imply it could be considered otherwise depending on context.
"We want our beliefs to be true, but if we don’t even know what they mean, we’re in trouble. A single sentence might be true in some sense, false in some other sense, and meaningless in a third. If you believe 'St. Trinian’s is a pretty little girls’ school,' what do you believe?"
When someone claims they believe that statement, they have a meaning in mind. Amphiboly is a feature of syntax and spoken language, not beliefs. Confusion, on the other hand, is.
"In 'the eggplant is a fruit,' probably what is meant is that all eggplants are fruits. In 'the dog is a Samoyed,' probably what is meant is that some dog is a Samoyed."
What he's describing is equivocation. However, something similar occurs when words or phrases are analogical (for example "healthy body" vs. "healthy sandwich"). Which brings me to...
"This problem is pervasive. Linguists catalog many distinct ways a sentence can be ambiguous. On analysis, almost any sentence can be read with multiple meanings. [...] natural languages—English, Chinese, Tamil—are hopelessly broken. They are incapable of adequately expressing true beliefs."
Why broken? By what measure? And why? That we must grapple with ambiguities doesn't mean natural language isn't serving its proper purpose. And incapable? I do hope that's hyperbole because, as the author has no doubt noticed, the entire article, including the quoted claim, is written in English.
"Modern rationalism’s first major improvement on traditional logic replaced natural language sentences with mathematical formulae."
Modern rationalism? Also formal languages can help, but they aren't magic bullets. I am still vulnerable to equivocation.
And why the dismissal of Aristotelian logic for which the author offers no tangible justification, like:
"Frege’s 1879 invention of modern formal logic fixed several outstanding defects in traditional, Aristotelian logic"
"Outstanding defects" is, to riff on the article's fixation, ambiguous. Three features of Aristotelian term logic that Fred Sommers identifies as "missing" are the inability to deal with particulars in a systematic way, the absence of relations and the absence of compound propositions. If those are defects, then fine, but even without those features, the logic is immensely useful in a broad range of applications. Also, recall that it dominated logic for two millennia (I highly recommend (Joyce 1916)). I think it deserves a bit more credit. Furthermore, Sommers updated term logic with his own "algebraized" term functor logic which accounts for these three "deficits". Worth also noting is that Sommers saw Fregean logic as a regression to Platonic views of subject and predicate and rejects putting them in separate universes (Sommers 1982).
"He solved several long-standing technical problems, in which Aristotelian logic gave outright wrong answers"
Wrong answers? Like?
"In Fregean epistemology, we can eliminate the ambiguity of 'is' [examples follows]"
How does that depart from the copula in term logic in any relevant way? Chapman's examples transcribed into term logic are "every Eggplant is a Fruit" and "some Dog is a Samoyed". Each is governed by laws of immediate inference. So what ambiguity is he talking about here that his FOL examples don't also suffer from?
"But what if you see a dog, and it’s obviously a Samoyed, but you don’t know its registry number? What do you believe then?"
> I dropped the hammer on the table and it smashed
> I dropped the vase on the table and it smashed
Exact same grammatical structure but if you switch the noun the way you parse the sentence changes. This is why machine learning with huge datasets wins in NLP, translation etc.