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”.
Depends upon what the meaning of the word “is” is
21–30 of 62 posts
Re: Depends upon what the meaning of the word “is” is
#22bill clinton, is that you?! 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…
> bill clinton, is that you?!
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.
Re: Depends upon what the meaning of the word “is” is
#23Todays sneak-peak at dilettantism in the philosophy of language, logic, and formal semantics. Brought to you by YC!
Re: Depends upon what the meaning of the word “is” is
#24One 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. - ‘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…
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.
Re: Depends upon what the meaning of the word “is” is
#25"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?"
You believe exactly what you've described.
Re: Depends upon what the meaning of the word “is” is
#26One 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. - ‘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…
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?
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.
Re: Depends upon what the meaning of the word “is” is
#27So Bill Clinton invented n-categories huh
Re: Depends upon what the meaning of the word “is” is
#28Earlier quoted context omitted.
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.
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Re: Depends upon what the meaning of the word “is” is
#29Forgive the dumb question but what is False about ‘∀x eggplant(x) ⇒ fruit(x)’
Re: Depends upon what the meaning of the word “is” is
#30Earlier quoted context omitted.
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: [S [DP [D The [N company]]] [VP [AuxP [Aux couldn't] [V make]] [DP [D the] [NP [N car] [AdjP [Adv fast] [A enough]]]] vs [S [DP [D The [N company]]] [V' [VP [AuxP [Aux couldn't] [V make]] [DP [D the] [N car]]] [AdjP [Adv fast] [A enough]]]…
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…
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.