In formal semantics, homogeneity is the phenomenon where

plural In many languages, a plural (sometimes list of glossing abbreviations, abbreviated as pl., pl, , or ), is one of the values of the grammatical number, grammatical category of number. The plural of a noun typically denotes a quantity greater than ...

expressions that seem to mean "all" negate to "none" rather than "not all". For example, the English sentence "Robin read the books" requires Robin to have read all of the books, while "Robin didn't read the books" requires her to have read none of them. Neither sentence is true if she read exactly half of the books. Homogeneity effects have been observed in a variety of languages including Japanese, Russian, and Hungarian. Semanticists have proposed a variety of explanations for homogeneity, often involving a combination of

presupposition In linguistics and philosophy, a presupposition is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse. Examples of presuppositions include: * ''Jane no longer writes ...

plural quantification In mathematics and mathematical logic, logic, plural quantification is the theory that an individual Variable (mathematics), variable x may take on ''plural'', as well as singular, values. As well as substituting individual objects such as Alice, ...

, and trivalent logics. Because analogous effects have been observed with

conditionals Conditional (if then) may refer to: *Causal conditional, if X then Y, where X is a cause of Y *Conditional probability, the probability of an event A given that another event B *Conditional proof, in logic: a proof that asserts a conditional, a ...

and other modal expressions, some semanticists have proposed that these phenomena involve pluralities of

possible worlds Possible Worlds may refer to: * Possible worlds, concept in philosophy * ''Possible Worlds'' (play), 1990 play by John Mighton ** ''Possible Worlds'' (film), 2000 film by Robert Lepage, based on the play * Possible Worlds (studio) * ''Possible ...

Overview

Homogeneous interpretations arise when a

expression seems to mean "all" when asserted but "none" when negated. For example, the English sentence in (1a) is typically interpreted to mean that Robin read all the books, while (1b) is interpreted to mean that she read none of them. This is a puzzle since (1b) would merely mean that some books went unread if "the books" expressed

universal quantification In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", "for every", or "given an arbitrary element". It expresses that a predicate can be satisfied by e ...

, as it appears to do in the positive sentence. :(1) Homogeneity with definite plurals: ::a. Robin read the books. ::b. Robin didn't read the books. Homogeneous readings are also possible with other expressions including conjunctions and bare plurals. For instance, (2a) means that Robin read both books while (2b) means that she read neither; example (3a) means that in general Robin likes books while (3b) means that in general she does not. :(2) Homogeneity with conjunctions: ::a. Robin read Syntactic Structures and Twilight. ::b. Robin didn't read Syntactic Structures and Twilight. :(3) Homogeneity with bare plurals: ::a. Robin likes books. ::b. Robin doesn't like books. Homogeneity effects have been studied in a variety of languages including English, Russian, Japanese and Hungarian. For instance, the Hungarian example in (4) behaves analogously to the English one in (1b). :(4) Nem látta a lányokat. ::"He didn’t see the girls"

Suspensions

Homogeneity can be suspended in certain circumstances. For instance, the definite plurals in (1) lose their homogeneous interpretation when an overt universal quantifier is inserted, as shown in (5). :(5) No Homogeneity with "all" and a definite plural: ::a. Robin read all the books ::b. Robin didn’t read all the books Additionally, the conjunctions in (3) lose their homogeneous interpretation when the connective receives

focus Focus (: foci or focuses) may refer to: Arts * Focus or Focus Festival, former name of the Adelaide Fringe arts festival in East Australia Film *Focus (2001 film), ''Focus'' (2001 film), a 2001 film based on the Arthur Miller novel *Focus (2015 ...

. :(6) Homogeneity with conjunctions: ::a. Robin read Syntactic Structures AND Twilight. ::b. Robin didn't read Syntactic Structures AND Twilight.

Theories

Homogeneity is important to semantic theory in part because it results in apparent

truth value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in ...

gaps. For example, neither of the sentences in (1) are assertable if Robin read exactly half of the relevant books. As a result, some linguists have attempted to provide unified analyses with other gappy phenomena such as

scalar implicature In pragmatics, scalar implicature, or quantity implicature, is an implicature that attributes an ''implicit'' meaning beyond the explicit or ''literal'' meaning of an utterance, and which suggests that the utterer had a reason for not using a more ...

free choice inference Free choice is a phenomenon in natural language where a linguistic disjunction appears to receive a logical conjunctive interpretation when it interacts with a modal operator. For example, the following English sentences can be interpreted to me ...

s, and

vagueness In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word " prime" ...

. Homogeneity effects have been argued to appear with semantic types other than individuals. For instance, negated conditionals and modals have been argued to show similar effects, potentially suggesting that they refer to pluralities of

possible world A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their met ...

References

Semantics Philosophical logic Formal semantics (natural language) {{Formal semantics

Overview

Suspensions

Theories

See also

References