On the Logic of Classes as Many View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2002-04

AUTHORS

Nino B. Cocchiarella

ABSTRACT

The notion of a "class as many" was central to Bertrand Russell's early form of logicism in his 1903 Principles of Mathematics. There is no empty class in this sense, and the singleton of an urelement (or atom in our reconstruction) is identical with that urelement. Also, classes with more than one member are merely pluralities — or what are sometimes called "plural objects" — and cannot as such be themselves members of classes. Russell did not formally develop this notion of a class but used it only informally. In what follows, we give a formal, logical reconstruction of the logic of classes as many as pluralities (or plural objects) within a fragment of the framework of conceptual realism. We also take groups to be classes as many with two or more members and show how groups provide a semantics for plural quantifier phrases. More... »

PAGES

303-338

References to SciGraph publications

  • 1996. Conceptual Realism as a Formal Ontology in FORMAL ONTOLOGY
  • 1998-02. Reference in Conceptual Realism in SYNTHESE
  • 2001-12. A Temporal Logic for Sortals in STUDIA LOGICA
  • 1989-03. Conceptualism, realism, and intensional logic in TOPOI
  • 2000-12. Sets and Classes as Many in JOURNAL OF PHILOSOPHICAL LOGIC
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1015190829525

    DOI

    http://dx.doi.org/10.1023/a:1015190829525

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1013742616


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0802", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Computation Theory and Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information and Computing Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "name": [
                "Department of Philosophy, Indiana University, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Cocchiarella", 
            "givenName": "Nino B.", 
            "id": "sg:person.01230062301.13", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01230062301.13"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf00138676", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007117900", 
              "https://doi.org/10.1007/bf00138676"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00138676", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007117900", 
              "https://doi.org/10.1007/bf00138676"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1013840126121", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009207177", 
              "https://doi.org/10.1023/a:1013840126121"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1026564222011", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1011065297", 
              "https://doi.org/10.1023/a:1026564222011"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-015-8733-4_2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1020239627", 
              "https://doi.org/10.1007/978-94-015-8733-4_2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1005005113229", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049673386", 
              "https://doi.org/10.1023/a:1005005113229"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/2026308", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069704636"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2002-04", 
        "datePublishedReg": "2002-04-01", 
        "description": "The notion of a \"class as many\" was central to Bertrand Russell's early form of logicism in his 1903 Principles of Mathematics. There is no empty class in this sense, and the singleton of an urelement (or atom in our reconstruction) is identical with that urelement. Also, classes with more than one member are merely pluralities \u2014 or what are sometimes called \"plural objects\" \u2014 and cannot as such be themselves members of classes. Russell did not formally develop this notion of a class but used it only informally. In what follows, we give a formal, logical reconstruction of the logic of classes as many as pluralities (or plural objects) within a fragment of the framework of conceptual realism. We also take groups to be classes as many with two or more members and show how groups provide a semantics for plural quantifier phrases.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1023/a:1015190829525", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1051009", 
            "issn": [
              "0039-3215", 
              "1572-8730"
            ], 
            "name": "Studia Logica", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "70"
          }
        ], 
        "name": "On the Logic of Classes as Many", 
        "pagination": "303-338", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "4177c21b0afae87e5c17b256751086bd9ed366cf94e22819d57aa5149570467a"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1023/a:1015190829525"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1013742616"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1023/a:1015190829525", 
          "https://app.dimensions.ai/details/publication/pub.1013742616"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T14:07", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8660_00000504.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1023/A:1015190829525"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1023/a:1015190829525'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1023/a:1015190829525'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1015190829525'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1015190829525'


     

    This table displays all metadata directly associated to this object as RDF triples.

    83 TRIPLES      21 PREDICATES      33 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1023/a:1015190829525 schema:about anzsrc-for:08
    2 anzsrc-for:0802
    3 schema:author N0274d96e48794f58b3f53bd41fe8de50
    4 schema:citation sg:pub.10.1007/978-94-015-8733-4_2
    5 sg:pub.10.1007/bf00138676
    6 sg:pub.10.1023/a:1005005113229
    7 sg:pub.10.1023/a:1013840126121
    8 sg:pub.10.1023/a:1026564222011
    9 https://doi.org/10.2307/2026308
    10 schema:datePublished 2002-04
    11 schema:datePublishedReg 2002-04-01
    12 schema:description The notion of a "class as many" was central to Bertrand Russell's early form of logicism in his 1903 Principles of Mathematics. There is no empty class in this sense, and the singleton of an urelement (or atom in our reconstruction) is identical with that urelement. Also, classes with more than one member are merely pluralities — or what are sometimes called "plural objects" — and cannot as such be themselves members of classes. Russell did not formally develop this notion of a class but used it only informally. In what follows, we give a formal, logical reconstruction of the logic of classes as many as pluralities (or plural objects) within a fragment of the framework of conceptual realism. We also take groups to be classes as many with two or more members and show how groups provide a semantics for plural quantifier phrases.
    13 schema:genre research_article
    14 schema:inLanguage en
    15 schema:isAccessibleForFree false
    16 schema:isPartOf N2b6af96e4d8246ab89d3a2362fdeea9b
    17 Nb068a14a3a11432dabff1c65dcd667f7
    18 sg:journal.1051009
    19 schema:name On the Logic of Classes as Many
    20 schema:pagination 303-338
    21 schema:productId N43ff6e69de75473795cc452f4bb681fe
    22 Na89fa88852fe4e71a2d69192fb9f51e5
    23 Nece6279129bf4883b40dc31a43d0255e
    24 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013742616
    25 https://doi.org/10.1023/a:1015190829525
    26 schema:sdDatePublished 2019-04-10T14:07
    27 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    28 schema:sdPublisher N9c3ad118ba224ad389e60f399f054d24
    29 schema:url http://link.springer.com/10.1023/A:1015190829525
    30 sgo:license sg:explorer/license/
    31 sgo:sdDataset articles
    32 rdf:type schema:ScholarlyArticle
    33 N0274d96e48794f58b3f53bd41fe8de50 rdf:first sg:person.01230062301.13
    34 rdf:rest rdf:nil
    35 N2b6af96e4d8246ab89d3a2362fdeea9b schema:volumeNumber 70
    36 rdf:type schema:PublicationVolume
    37 N43ff6e69de75473795cc452f4bb681fe schema:name dimensions_id
    38 schema:value pub.1013742616
    39 rdf:type schema:PropertyValue
    40 N9c3ad118ba224ad389e60f399f054d24 schema:name Springer Nature - SN SciGraph project
    41 rdf:type schema:Organization
    42 Na3e08f529d564cdbabf0db9c0dcab684 schema:name Department of Philosophy, Indiana University, USA
    43 rdf:type schema:Organization
    44 Na89fa88852fe4e71a2d69192fb9f51e5 schema:name doi
    45 schema:value 10.1023/a:1015190829525
    46 rdf:type schema:PropertyValue
    47 Nb068a14a3a11432dabff1c65dcd667f7 schema:issueNumber 3
    48 rdf:type schema:PublicationIssue
    49 Nece6279129bf4883b40dc31a43d0255e schema:name readcube_id
    50 schema:value 4177c21b0afae87e5c17b256751086bd9ed366cf94e22819d57aa5149570467a
    51 rdf:type schema:PropertyValue
    52 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    53 schema:name Information and Computing Sciences
    54 rdf:type schema:DefinedTerm
    55 anzsrc-for:0802 schema:inDefinedTermSet anzsrc-for:
    56 schema:name Computation Theory and Mathematics
    57 rdf:type schema:DefinedTerm
    58 sg:journal.1051009 schema:issn 0039-3215
    59 1572-8730
    60 schema:name Studia Logica
    61 rdf:type schema:Periodical
    62 sg:person.01230062301.13 schema:affiliation Na3e08f529d564cdbabf0db9c0dcab684
    63 schema:familyName Cocchiarella
    64 schema:givenName Nino B.
    65 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01230062301.13
    66 rdf:type schema:Person
    67 sg:pub.10.1007/978-94-015-8733-4_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1020239627
    68 https://doi.org/10.1007/978-94-015-8733-4_2
    69 rdf:type schema:CreativeWork
    70 sg:pub.10.1007/bf00138676 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007117900
    71 https://doi.org/10.1007/bf00138676
    72 rdf:type schema:CreativeWork
    73 sg:pub.10.1023/a:1005005113229 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049673386
    74 https://doi.org/10.1023/a:1005005113229
    75 rdf:type schema:CreativeWork
    76 sg:pub.10.1023/a:1013840126121 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009207177
    77 https://doi.org/10.1023/a:1013840126121
    78 rdf:type schema:CreativeWork
    79 sg:pub.10.1023/a:1026564222011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011065297
    80 https://doi.org/10.1023/a:1026564222011
    81 rdf:type schema:CreativeWork
    82 https://doi.org/10.2307/2026308 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069704636
    83 rdf:type schema:CreativeWork
     




    Preview window. Press ESC to close (or click here)


    ...