Switch to: References

Citations of:

Numbers and Manifolds

In Barry Smith (ed.), Parts and Moments. Studies in Logic and Formal Ontology. Philosophia Verlag. pp. 160-197 (1982)

Add citations

You must login to add citations.
  1. What is Frege's Relativity Argument?Palle Yourgrau - 1997 - Canadian Journal of Philosophy 27 (2):137-172.
    Sets are multitudes which are also unities. It is surprising that the fact that multitudes are also unities leads to no contradictions: this is the main fact of mathematics.Kurt Gödel (Hao Wang,A Logical Journey: From Gödel to Philosophy)In what sense can something be at the same time one and many? The problem is familiar since Plato (for example,Republic524e). In recent times, Whitehead and Russell, inPrincipia Mathematica,have been struck by the difficulty of the problem: ‘If there is such an object as (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • The logic and meaning of plurals. Part II.Byeong-uk Yi - 2006 - Journal of Philosophical Logic 35 (3):239-288.
    In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the (...)
    Download  
     
    Export citation  
     
    Bookmark   83 citations  
  • In defence of Higher-Level Plural Logic: drawing conclusions from natural language.Berta Grimau - 2019 - Synthese 198 (6):5253-5280.
    Plural Logic is an extension of First-Order Logic which has, as well as singular terms and quantifiers, their plural counterparts. Analogously, Higher-Level Plural Logic is an extension of Plural Logic which has, as well as plural terms and quantifiers, higher-level plural ones. Roughly speaking, higher-level plurals stand to plurals like plurals stand to singulars; they are pluralised plurals. Allegedly, Higher-Level Plural Logic enjoys the expressive power of a simple type theory while committing us to nothing more than the austere ontology (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Groups as pluralities.John Horden & Dan López de Sa - 2020 - Synthese 198 (11):10237-10271.
    We say that each social group is identical to its members. The group just is them; they just are the group. This view of groups as pluralities has tended to be swiftly rejected by social metaphysicians, if considered at all, mainly on the basis of two objections. First, it is argued that groups can change in membership, while pluralities cannot. Second, it is argued that different groups can have exactly the same members, while different pluralities cannot. We rebut these objections, (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • Plural descriptions and many-valued functions.Alex Oliver & Timothy Smiley - 2005 - Mind 114 (456):1039-1068.
    Russell had two theories of definite descriptions: one for singular descriptions, another for plural descriptions. We chart its development, in which ‘On Denoting’ plays a part but not the part one might expect, before explaining why it eventually fails. We go on to consider many-valued functions, since they too bring in plural terms—terms such as ‘4’ or the descriptive ‘the inhabitants of London’ which, like plain plural descriptions, stand for more than one thing. Logicians need to take plural reference seriously (...)
    Download  
     
    Export citation  
     
    Bookmark   26 citations