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6

The key to understanding is the difference between objects and names of objects: A meronom is a part. A meronym is the name of a part. A meronomy is a relationship between parts and sub-parts. Meronymy is a relationship between words. Mereology is the mathematical study of parts and wholes. It cares about mathematical objects, not about words. The kind ...


6

You (and the source) are confusing the technical and colloquial sense of the word logic here. When you say There's a certain logic to language. or Even language is logical. you're saying something like, The way language works make sense. But this is radically different from saying, Language can be described using the apparatus of formal logic. Most ...


5

In the philosophy of language and modal logic, the conceptions you label "static" and "dynamic" are called rigid designator and flaccid designator respecively.


5

The semicolon in ∀;y is surely a typo. It should just be ∀y, just like the ∀x that precedes it. A period is often used to introduce the scope of a variable binding expression like ∀x, e.g. ∀x.φ. By convention, the scope stretches all the way to the end of the entire expression. So, for example, in ∀x.Px ∧ Qx, the occurrence of x in Qx is bound by ∀x. That ...


4

Your question has some false presuppositions. In general, when trying to understand the historical relationship between words of English that seem to historically share a root, where Latin in the apparent source language and the subject matter is anything vaguely philosophical, you have to start with the actual origin, which is usually Greek. The relevant ...


4

In many languages, for example Bengali, the word comparable to if is optional and frequently absent, whereas the word marking the apodosis (usually with a similar function to then) is mandatory, exactly the opposite way round to English. Of course, it's dubious whether then has an inherent connection with conditionals in English.


3

There are two different answers, depending on the environment. In certain contexts (logical formulae, programming languages, legal documents, Magic: the Gathering cards), avoiding ambiguity is very important. So in these contexts, there'll be some external rule that tells you how to interpret ambiguities. For example, in Magic: the Gathering rules text, "or"...


3

Start with 2.: A unless B = A, if not B A, if not B = if not B then A In general, if x then y = not x or y (for the "material implication" of logic) So, if not B then A = not not B or A (from the above, with x as not B and y as A) In general, not not x = x So, not not B or A = B or A (substituting B for not not B) In general, x or y = y or x So, B or A = A ...


3

The English sentence "every man who owns a donkey beats it" can be interpreted as "every man beats every donkey that he owns", which makes no implication that anything exists. It is true even if there are no men, no donkeys, or no donkey slavery. This means a rigorous wording of this sentence uses only universal quantifiers ("for all&...


3

Your formula means that every man owns a donkey that he beats, which is not what the original sentence means.


3

You are addressing two problems: why is there, apparently, a monotonicity reversal when negating your first example ("banana"), but not the second ("driving")? why is your first example upward-monotonic, while the second is downward monotonic? The problem has to do with understanding that general terms like "fruit" or "driving" may refer to elements of ...


3

When glossing a logical proposition with English words, we are not really using the English language system; it's just a way to represent the unambiguous mathematical concepts in a mnemonic and easy-to-pronounce manner. For this reason, mathematicians and logicians like to present specialized definitions of the words they use. That is what is being done in ...


3

The roots of classical logic lie in Ancient Greece. Because of this, many Latin terms dealing with philosophy and logic were either taken from Greek, or modeled after the structure of Greek words (that is, calqued). So I thought that researching equivalent terms in Ancient Greek might shed light on your question. According to Etymonline, the pair of words ...


2

Yes, linear logic has close connections with Lambek/categorial grammar. The big picture is basically that, with respect to a Lambek/categorial grammar, a proof of the syntactic category of a phrase of a language corresponds to a proof in the logical (e.g. deductive) sense, and that the grammar itself corresponds to a certain substructural logic. As Morrill (...


2

There seem to be three issues here. (1) Why is "I sometimes pet bunnies" second order, in view of the fact that it seems to mean about the same as "I pet bunnies"? What is the second order logical form? (2) Reichenbach's idea about second order logic is that it involves quantifying over predicates. His example was "Napoleon had all the properties of a ...


2

David Lewis' account of the logic of imperatives is in terms of the possible worlds in which the imperative is obeyed. Here is a handout for a class which extensively deals with the formal semantics of questions. Anyhow, there is more to what linguists do than assign semantic interpretations to sentences. We use formalisms for all aspects of language, and ...


2

You need to bear in mind that logic textbooks do not purport to provide translations of natural language into logical symbolism. Instead, they provide conventialized translations of standard logical symbols and expressions of English. It is pretty standard that in Philosophy 150, about half the time students screw up the exercise of matching natural language ...


2

a) Correct. Some fine-tuning to your answer: The donkey that Jake owns in own(j,x), is not the same donkey that was beaten in beat(j,x). It is not necessarily the same. Depending on which assignment function the formula is evaluated under, the assignment for the second occurence of the variable x can co-incide with the one for the first x. But what is ...


2

The reason is as follows: For ALL we need "for all objects, if they are P, then they are also Q". If we would use logical AND, it would mean "for all objects, they are P and they are Q" which is obviously not what we want. For SOME we need "for some object, it is P and it is Q". If we would use implication, it would mean "for some object, if it is P, then ...


2

The wording of your question seems to imply an equivalence between first order predicate logic and higher order logics. They are not equivalent. First order predicate logic was shown to be consistent and complete by Kurt Gödel, but "Stronger logics, such as second-order logic, are not complete." (Consistency.) Whether first order predicate logic is ...


2

Yes. See Arc pair grammar....


2

As for the order of things: "In conditional statements, the conditional clause precedes the conclusion as the normal order in all languages. (...) (Greenberg 1963: 84, #14) (https://typo.uni-konstanz.de/raraneu/universals-archive/501/) As for the question if there are words for "if", "then" and "else" in all languages: No ...


2

Linguists generally distinguish literal entailment vs. pragmatic implicature. As for literal entailment, "A or B" mean "A or B" and if A and B both happen to be true, that's okay as well. But "Chicken or beef" literally is not a proposition and it has no truth value. However, the construction pragmatically implies "You are ...


2

In some theories of epistemology, the distinction between class and individual is not strict, for example the class "mammal" is composed of individuals such as "dog; cat; human; horse", and "horse" in turn is composed of numerous horses (some of whom have names, most of whom do not), or individual humans (most of whom have names)...


1

Predicate logic is an approximation of some functions of language, and does not cover all use cases. Traditionally, it doesn't really account for time (with just entities, there isn't a good way to distinguish past tense from future tense). I've seen some analyses that use predicate logic as a base add in a "time" variable to every verb (BAKE(x, y, t) = x ...


1

Bart said to Lisa that he would braid her hair today, but he chopped his hand off yesterday. (SAY (BART,           (INTEND (BART,                             (TODAY (BRAID (BART, LISA_HAIR)))))             &...


1

I'd recommend looking at Jerry Hobbs' way of parsing and representing English, it's one of the most elaborate ones when it comes to logic and commonsense representation: Jerry Hobbs: "Discourse and Inference"


1

If Ido coordinating conjunctions have ambiguous scope like English conjunctions, then it will be possible for logically coherent sentences to include sequences like "gratis vel not gratis" or "in the daytime vel in the nighttime." Let's consider the example "gratis [vel] not gratis books". In the corresponding English phrase "free or not free books", "free" ...


1

You have raised many questions here so I'm not sure which one is the best to answer first. Since there can be no universal ontology, the use of Cyc or some other KB depends its purpose. If, hypothetically, the purpose is to mimic natural language use in humans, then I think there is still a long way to go. This is, in no small part, because what you think ...


1

They're talking about section 1, not the complete set of all reality. This is called context. Presumably, the book goes on to explain why this rhetorical point is false.


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