Online research in philosophy

This paper introduces some of the main components of a novel type theoretical semantics for quantifi- cation with plural noun phrases. This theory, unlike previous ones, sticks to the standard generalized quantifier treatment of singular noun phrases and uses only one lifting operator per semantic category (predicate, quantifier and determiner) for quantification with plurals. Following Bennett (1974), plural individuals are treated as functions of type ¢¡ . Plural nouns and other plural predicates accordingly denote £ ¢¡¥¤¦¡ functions. Such predicates do not match the standard £ ¢¡¥¤ £§£ ¢¡¨¤©¡¥¤ type of determiners. Following Partee and Rooth (1983), type mismatches are resolved using type shifting operators. These operators derive collectivity with plurals, keeping the analysis of singular noun phrases, where no type mismatch arises, as in Barwise and Cooper (1981). A single type shifting operator for determiners combines into one reading the existential shift and the counting (neutral) shift of Scha (1981) and Van der Does (1993). This operator combines the conservativity principle of generalized quantifier theory with Szabolcsi’s (1997) existential quantification over witness sets. The unified lift prevents unmotivated ambiguity as well as the monotonicity ill of existential lifts pointed out by Van Benthem..

Background ideas -- Consequences -- Relations of support -- Logical consequence : the basic recipe -- Valid arguments and truth -- Language, form, and logical theories -- Language -- Atoms, connectives, and molecules -- Connectives and form -- Validity and form -- Language and formal languages -- Logical theories : rivalry -- Set-theoretic tools -- Sets -- Ordered sets : pairs and n-tuples -- Relations -- Functions -- Sets as tools -- Basic connectives -- Classical theory -- Cases : complete and consistent -- Classical truth conditions -- Basic classical consequence -- Motivation : precision -- Defined connectives -- Some notable valid forms -- A paracomplete theory -- Apparent unsettledness -- Cases : incomplete -- Paracomplete truth and falsity conditions -- Paracomplete consequence -- Defined connectives -- Some notable forms -- A paraconsistent theory -- Apparent overdeterminacy -- Cases : inconsistent -- Paraconsistent truth conditions -- Paraconsistent consequence -- Defined connectives -- Some notable forms -- Innards, identity, and quantifiers -- Atomic innards -- Atomic innards : names and predicates -- Truth and falsity conditions for atomics -- Cases, domains, and interpretation functions -- Classical, paracomplete, and paraconsistent -- Identity -- Logical expressions and logical form -- Validity involving identity -- Identity : informal sketch -- Truth conditions : informal sketch -- Everything and something -- Validity involving quantifiers -- Quantifiers : an informal sketch -- Truth and falsity conditions -- Paraconsistent, paracomplete, classical -- Freedom, necessity, and beyond -- Speaking freely -- Speaking of non-existent things -- Existential import -- Freeing our terms, expanding our domains -- Truth conditions : an informal sketch -- Possibilities -- Possibility and necessity -- Towards truth and falsity conditions -- Cases and consequence -- Remark on going beyond possibility -- Glimpsing different logical roads -- Other conditionals -- Other negations -- Other alethic modalities : actuality -- Same connectives, different truth conditions -- Another road to difference : consequence.

Singular-term semantics has been intractable. Frege took the referents of singular terms to be their semantic values. On his account, vacuous terms lacked values. Russell separated the semantics of definite descriptions from the semantics of proper names, which caused truth-values to be composed in two different ways and still left vacuous names without values. Montague gave all noun phrases sets of verb-phrase extensions for values, which created type mismatches when noun phrases were objects and still left vacuous names without values. There is a single type of value for all noun phrases that dissolves the difficulties which have beset singular-term semantics.

We study definability in terms of monotone generalized quantifiers satisfying Isomorphism Closure, Conservativity and Extension. Among the quantifiers with the latter three properties – here called CE quantifiers – one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number of are highly non-monotone. They are nevertheless definable in terms of monotone CE quantifiers: we give a necessary and sufficient condition for such definability. We further identify a stronger form of monotonicity, called smoothness, which also has linguistic relevance, and we extend our considerations to smooth quantifiers. The results lead us to propose two tentative universals concerning monotonicity and natural language quantification. The notions involved as well as our proofs are presented using a graphical representation of quantifiers in the so-called number triangle.

The eclipse riddle -- Seeing surfaces -- The disappearing act -- Spinning shadows -- Berkeley's shadow -- Para-reflections -- Para-refractions : shadowgrams and the black drop -- Goethe's colored shadows -- Filtows -- Holes in the light -- Black and blue -- Seeing in black and white -- We see in the dark -- Hearing silence.

When we utter sentences containing quantifiers, typically we are not to be taken to speak about absolutely everything there is. Suppose Mary has invited her friend John to a party to which she is going. If, upon entering the party, Mary turns to Jack and utters (1), it would be rather odd of Jack to object by pointing out that John in fact knows several people who are not present.

When we utter sentences containing quantifiers, typically we are not to be taken to speak about absolutely everything there is. Suppose Mary has invited her friend John to a party to which she is going. If, upon entering the party, Mary turns to Jack and utters (1), it would be rather odd of Jack to object by pointing out that John in fact knows several people who are not present.

Berkeley thinks that we only see the size, shape, location, and orientation of objects in virtue of the correlation between sight and touch. Shadows have all of these spatial properties and yet are intangible. In Seeing Dark Things (2008), Roy Sorensen argues that shadows provide a counterexample to Berkeley's theory of vision and, consequently, to his idealism. This paper shows that Berkeley can accept both that shadows are intangible and that they have spatial properties.

I discuss a solution to the Yale shadow puzzle, due to Roy Sorensen, based on the actual process theory of causation, and argue that it does not work in the case of a new version of the puzzle, which I call "the Bilkent shadow puzzle". I offer a picture of the ontology of shadows that constitute the basis for a new solution that uniformly applies to both puzzles.

The arguments that Fodor (1987: 150-52) gives in support of a Language of Thought are apparently straightforward. (1) Linguistic capacities are "systematic", in the sense that if one understands the words 'John loves Mary' one also understands the form of words 'Mary loves John'. In other words, sentences have a combinatorial semantics, because they have constituent structure. (2) If cognitive capacities are systematic in the same way, they must have constituent structure also. Thus there is a Language of Thought. The essential connection between language and thought that the argument requires is: Since the function of language is to express thought, to understand a sentence is to grasp the thought that its utterance standardly conveys. So from the systematicity of sentences it follows that anyone who can grasp the thought that John loves Mary can grasp the thought that Mary loves John. Thought must be as systematic as language, for the best empirical explanation of the psychological fact that one who grasps the thought that John loves Mary can grasp the thought that Mary loves John is that grasping a thought is standing in some thinking relation to a complex entity whose constituents are MARY, X LOVES Y, and JOHN and semantic relations among MARY, X LOVES Y, and JOHN. So sayeth Fodor (1987).